Solved on Jan 22, 2024

Solve for x in the following linear equations: $-1=\frac{-3+x}{14}$ , $-5+\frac{x}{2}=-17$ , $33=-7x-23$ , $\frac{1}{2}x-9=6$ , $6+5x=6$ , $-9x+1=-80$ , $-186=12+11x$ , $\frac{x+2}{3}=-5$ , $8x-11=-283$ , $-116=-11+7x$ .

STEP 1

Let's solve each equation step by step.
For equation 11: $-1=\frac{-3+x}{14}$
Multiply both sides of the equation by 14 to eliminate the fraction.
$-1 \times 14 = \left(\frac{-3+x}{14}\right) \times 14$

STEP 2

Simplify both sides of the equation.
$-14 = -3 + x$

STEP 3

Add 3 to both sides of the equation to isolate the variable $x$ .
$-14 + 3 = x$

STEP 4

Calculate the value of $x$ .
$x = -14 + 3 = -11$
For equation 12: $-5+\frac{x}{2}=-17$

STEP 5

Add 5 to both sides of the equation to isolate the fraction.
$-5 + 5 + \frac{x}{2} = -17 + 5$

STEP 6

Simplify both sides of the equation.
$\frac{x}{2} = -12$

STEP 7

Multiply both sides by 2 to solve for $x$ .
$2 \times \frac{x}{2} = -12 \times 2$

STEP 8

Calculate the value of $x$ .
$x = -24$
For equation 13: $33=-7x-23$

STEP 9

Add 23 to both sides of the equation to isolate the term with $x$ .
$33 + 23 = -7x - 23 + 23$

STEP 10

Simplify both sides of the equation.
$56 = -7x$

STEP 11

Divide both sides by -7 to solve for $x$ .
$\frac{56}{-7} = \frac{-7x}{-7}$

STEP 12

Calculate the value of $x$ .
$x = -8$
For equation 14: $\frac{1}{2}x - 9 = 6$

STEP 13

Add 9 to both sides of the equation to isolate the fraction.
$\frac{1}{2}x - 9 + 9 = 6 + 9$

STEP 14

Simplify both sides of the equation.
$\frac{1}{2}x = 15$

STEP 15

Multiply both sides by 2 to solve for $x$ .
$2 \times \frac{1}{2}x = 15 \times 2$

STEP 16

Calculate the value of $x$ .
$x = 30$
For equation 15: $6+5x=6$

STEP 17

Subtract 6 from both sides of the equation to isolate the term with $x$ .
$6 - 6 + 5x = 6 - 6$

STEP 18

Simplify both sides of the equation.
$5x = 0$

STEP 19

Divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{0}{5}$

STEP 20

Calculate the value of $x$ .
$x = 0$
For equation 16: $-9x+1=-80$

STEP 21

Subtract 1 from both sides of the equation to isolate the term with $x$ .
$-9x + 1 - 1 = -80 - 1$

STEP 22

Simplify both sides of the equation.
$-9x = -81$

STEP 23

Divide both sides by -9 to solve for $x$ .
$\frac{-9x}{-9} = \frac{-81}{-9}$

STEP 24

Calculate the value of $x$ .
$x = 9$
For equation 17: $-186=12+11x$

STEP 25

Subtract 12 from both sides of the equation to isolate the term with $x$ .
$-186 - 12 = 12 - 12 + 11x$

STEP 26

Simplify both sides of the equation.
$-198 = 11x$

STEP 27

Divide both sides by 11 to solve for $x$ .
$\frac{-198}{11} = \frac{11x}{11}$

STEP 28

Calculate the value of $x$ .
$x = -18$
For equation 18: $\frac{x+2}{3}=-5$

STEP 29

Multiply both sides by 3 to eliminate the fraction.
$3 \times \frac{x+2}{3} = -5 \times 3$

STEP 30

Simplify both sides of the equation.
$x + 2 = -15$

STEP 31

Subtract 2 from both sides to solve for $x$ .
$x = -15 - 2$

STEP 32

Calculate the value of $x$ .
$x = -17$
For equation 19: $8x-11=-283$

STEP 33

Add 11 to both sides of the equation to isolate the term with $x$ .
$8x - 11 + 11 = -283 + 11$

STEP 34

Simplify both sides of the equation.
$8x = -272$

STEP 35

Divide both sides by 8 to solve for $x$ .
$\frac{8x}{8} = \frac{-272}{8}$

STEP 36

Calculate the value of $x$ .
$x = -34$
For equation 20: $-116=-11+7x$

STEP 37

Add 11 to both sides of the equation to isolate the term with $x$ .
$-116 + 11 = -11 + 11 + 7x$

STEP 38

Simplify both sides of the equation.
$-105 = 7x$

STEP 39

Divide both sides by 7 to solve for $x$ .
$\frac{-105}{7} = \frac{7x}{7}$

STEP 40

Calculate the value of $x$ .
$x = -15$
The solutions for the equations are as follows:
11. $x = -11$
12. $x = -24$
13. $x = -8$
14. $x = 30$
15. $x = 0$
16. $x = 9$
17. $x = -18$
18. $x = -17$
19. $x = -34$
20. $x = -15$

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STEP 1

Let's solve each equation step by step.For equation 11: −1=−3+x14-1=\frac{-3+x}{14}−1=14−3+x​Multiply both sides of the equation by 14 to eliminate the fraction.−1×14=(−3+x14)×14-1 \times 14 = \left(\frac{-3+x}{14}\right) \times 14−1×14=(14−3+x​)×14

STEP 2

Simplify both sides of the equation.−14=−3+x-14 = -3 + x−14=−3+x

STEP 3

Add 3 to both sides of the equation to isolate the variable xxx.−14+3=x-14 + 3 = x−14+3=x

STEP 4

Calculate the value of xxx.x=−14+3=−11x = -14 + 3 = -11x=−14+3=−11For equation 12: −5+x2=−17-5+\frac{x}{2}=-17−5+2x​=−17

STEP 5

Add 5 to both sides of the equation to isolate the fraction.−5+5+x2=−17+5-5 + 5 + \frac{x}{2} = -17 + 5−5+5+2x​=−17+5

STEP 6

Simplify both sides of the equation.x2=−12\frac{x}{2} = -122x​=−12

STEP 7

Multiply both sides by 2 to solve for xxx.2×x2=−12×22 \times \frac{x}{2} = -12 \times 22×2x​=−12×2

STEP 8

Calculate the value of xxx.x=−24x = -24x=−24For equation 13: 33=−7x−2333=-7x-2333=−7x−23

STEP 9

Add 23 to both sides of the equation to isolate the term with xxx.33+23=−7x−23+2333 + 23 = -7x - 23 + 2333+23=−7x−23+23

STEP 10

Simplify both sides of the equation.56=−7x56 = -7x56=−7x

STEP 11

Divide both sides by -7 to solve for xxx.56−7=−7x−7\frac{56}{-7} = \frac{-7x}{-7}−756​=−7−7x​

STEP 12

Calculate the value of xxx.x=−8x = -8x=−8For equation 14: 12x−9=6\frac{1}{2}x - 9 = 621​x−9=6

STEP 13

Add 9 to both sides of the equation to isolate the fraction.12x−9+9=6+9\frac{1}{2}x - 9 + 9 = 6 + 921​x−9+9=6+9

STEP 14

Simplify both sides of the equation.12x=15\frac{1}{2}x = 1521​x=15

STEP 15

Multiply both sides by 2 to solve for xxx.2×12x=15×22 \times \frac{1}{2}x = 15 \times 22×21​x=15×2

STEP 16

Calculate the value of xxx.x=30x = 30x=30For equation 15: 6+5x=66+5x=66+5x=6

STEP 17

Subtract 6 from both sides of the equation to isolate the term with xxx.6−6+5x=6−66 - 6 + 5x = 6 - 66−6+5x=6−6

STEP 18

Simplify both sides of the equation.5x=05x = 05x=0

STEP 19

Divide both sides by 5 to solve for xxx.5x5=05\frac{5x}{5} = \frac{0}{5}55x​=50​

STEP 20

Calculate the value of xxx.x=0x = 0x=0For equation 16: −9x+1=−80-9x+1=-80−9x+1=−80

STEP 21

Subtract 1 from both sides of the equation to isolate the term with xxx.−9x+1−1=−80−1-9x + 1 - 1 = -80 - 1−9x+1−1=−80−1

STEP 22

Simplify both sides of the equation.−9x=−81-9x = -81−9x=−81

STEP 23

Divide both sides by -9 to solve for xxx.−9x−9=−81−9\frac{-9x}{-9} = \frac{-81}{-9}−9−9x​=−9−81​

STEP 24

Calculate the value of xxx.x=9x = 9x=9For equation 17: −186=12+11x-186=12+11x−186=12+11x

STEP 25

Subtract 12 from both sides of the equation to isolate the term with xxx.−186−12=12−12+11x-186 - 12 = 12 - 12 + 11x−186−12=12−12+11x

STEP 26

Simplify both sides of the equation.−198=11x-198 = 11x−198=11x

STEP 27

Divide both sides by 11 to solve for xxx.−19811=11x11\frac{-198}{11} = \frac{11x}{11}11−198​=1111x​

STEP 28

Calculate the value of xxx.x=−18x = -18x=−18For equation 18: x+23=−5\frac{x+2}{3}=-53x+2​=−5

STEP 29

Multiply both sides by 3 to eliminate the fraction.3×x+23=−5×33 \times \frac{x+2}{3} = -5 \times 33×3x+2​=−5×3

STEP 30

Simplify both sides of the equation.x+2=−15x + 2 = -15x+2=−15

STEP 31

Subtract 2 from both sides to solve for xxx.x=−15−2x = -15 - 2x=−15−2

STEP 32

Calculate the value of xxx.x=−17x = -17x=−17For equation 19: 8x−11=−2838x-11=-2838x−11=−283

STEP 33

Add 11 to both sides of the equation to isolate the term with xxx.8x−11+11=−283+118x - 11 + 11 = -283 + 118x−11+11=−283+11

STEP 34

Simplify both sides of the equation.8x=−2728x = -2728x=−272

STEP 35

Divide both sides by 8 to solve for xxx.8x8=−2728\frac{8x}{8} = \frac{-272}{8}88x​=8−272​

STEP 36

Calculate the value of xxx.x=−34x = -34x=−34For equation 20: −116=−11+7x-116=-11+7x−116=−11+7x

STEP 37

Add 11 to both sides of the equation to isolate the term with xxx.−116+11=−11+11+7x-116 + 11 = -11 + 11 + 7x−116+11=−11+11+7x

STEP 38

Simplify both sides of the equation.−105=7x-105 = 7x−105=7x

STEP 39

Divide both sides by 7 to solve for xxx.−1057=7x7\frac{-105}{7} = \frac{7x}{7}7−105​=77x​

STEP 40

Start learning now

Let's solve each equation step by step.
For equation 11: $-1=\frac{-3+x}{14}$
Multiply both sides of the equation by 14 to eliminate the fraction.
$-1 \times 14 = \left(\frac{-3+x}{14}\right) \times 14$

Simplify both sides of the equation.
$-14 = -3 + x$

Add 3 to both sides of the equation to isolate the variable $x$ .
$-14 + 3 = x$

Calculate the value of $x$ .
$x = -14 + 3 = -11$
For equation 12: $-5+\frac{x}{2}=-17$

Add 5 to both sides of the equation to isolate the fraction.
$-5 + 5 + \frac{x}{2} = -17 + 5$

Simplify both sides of the equation.
$\frac{x}{2} = -12$

Multiply both sides by 2 to solve for $x$ .
$2 \times \frac{x}{2} = -12 \times 2$

Calculate the value of $x$ .
$x = -24$
For equation 13: $33=-7x-23$

Add 23 to both sides of the equation to isolate the term with $x$ .
$33 + 23 = -7x - 23 + 23$

Simplify both sides of the equation.
$56 = -7x$

Divide both sides by -7 to solve for $x$ .
$\frac{56}{-7} = \frac{-7x}{-7}$

Calculate the value of $x$ .
$x = -8$
For equation 14: $\frac{1}{2}x - 9 = 6$

Add 9 to both sides of the equation to isolate the fraction.
$\frac{1}{2}x - 9 + 9 = 6 + 9$

Simplify both sides of the equation.
$\frac{1}{2}x = 15$

Multiply both sides by 2 to solve for $x$ .
$2 \times \frac{1}{2}x = 15 \times 2$

Calculate the value of $x$ .
$x = 30$
For equation 15: $6+5x=6$

Subtract 6 from both sides of the equation to isolate the term with $x$ .
$6 - 6 + 5x = 6 - 6$

Simplify both sides of the equation.
$5x = 0$

Divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{0}{5}$

Calculate the value of $x$ .
$x = 0$
For equation 16: $-9x+1=-80$

Subtract 1 from both sides of the equation to isolate the term with $x$ .
$-9x + 1 - 1 = -80 - 1$

Simplify both sides of the equation.
$-9x = -81$

Divide both sides by -9 to solve for $x$ .
$\frac{-9x}{-9} = \frac{-81}{-9}$

Calculate the value of $x$ .
$x = 9$
For equation 17: $-186=12+11x$

Subtract 12 from both sides of the equation to isolate the term with $x$ .
$-186 - 12 = 12 - 12 + 11x$

Simplify both sides of the equation.
$-198 = 11x$

Divide both sides by 11 to solve for $x$ .
$\frac{-198}{11} = \frac{11x}{11}$

Calculate the value of $x$ .
$x = -18$
For equation 18: $\frac{x+2}{3}=-5$

Multiply both sides by 3 to eliminate the fraction.
$3 \times \frac{x+2}{3} = -5 \times 3$

Simplify both sides of the equation.
$x + 2 = -15$

Subtract 2 from both sides to solve for $x$ .
$x = -15 - 2$

Calculate the value of $x$ .
$x = -17$
For equation 19: $8x-11=-283$

Add 11 to both sides of the equation to isolate the term with $x$ .
$8x - 11 + 11 = -283 + 11$

Simplify both sides of the equation.
$8x = -272$

Divide both sides by 8 to solve for $x$ .
$\frac{8x}{8} = \frac{-272}{8}$

Calculate the value of $x$ .
$x = -34$
For equation 20: $-116=-11+7x$

Add 11 to both sides of the equation to isolate the term with $x$ .
$-116 + 11 = -11 + 11 + 7x$

Simplify both sides of the equation.
$-105 = 7x$

Divide both sides by 7 to solve for $x$ .
$\frac{-105}{7} = \frac{7x}{7}$