Solved on Jan 18, 2024

Solve for $x$ in the following linear equations: $x+x+x+3=15$ , $6x+11+5x=66$ , $6x-3=4x+9$ .

STEP 1

Assumptions
1. We are solving linear equations with one variable, $x$ .
2. The goal is to isolate $x$ on one side of the equation to find its value.
Problem 22: $x + x + x + 3 = 15$

STEP 2

Combine like terms on the left side of the equation.
$3x + 3 = 15$

STEP 3

Subtract 3 from both sides of the equation to isolate the term with $x$ .
$3x + 3 - 3 = 15 - 3$

STEP 4

Simplify both sides of the equation.
$3x = 12$

STEP 5

Divide both sides of the equation by 3 to solve for $x$ .
$\frac{3x}{3} = \frac{12}{3}$

STEP 6

Calculate the value of $x$ .
$x = 4$
Problem 25: $6x + 11 + 5x = 66$

STEP 7

Combine like terms on the left side of the equation.
$11x + 11 = 66$

STEP 8

Subtract 11 from both sides of the equation to isolate the term with $x$ .
$11x + 11 - 11 = 66 - 11$

STEP 9

Simplify both sides of the equation.
$11x = 55$

STEP 10

Divide both sides of the equation by 11 to solve for $x$ .
$\frac{11x}{11} = \frac{55}{11}$

STEP 11

Calculate the value of $x$ .
$x = 5$
Problem 28: $6x - 3 = 4x + 9$

STEP 12

Subtract $4x$ from both sides of the equation to get all terms with $x$ on one side.
$6x - 4x - 3 = 4x - 4x + 9$

STEP 13

Simplify both sides of the equation.
$2x - 3 = 9$

STEP 14

Add 3 to both sides of the equation to isolate the term with $x$ .
$2x - 3 + 3 = 9 + 3$

STEP 15

Simplify both sides of the equation.
$2x = 12$

STEP 16

Divide both sides of the equation by 2 to solve for $x$ .
$\frac{2x}{2} = \frac{12}{2}$

STEP 17

Calculate the value of $x$ .
$x = 6$
Solutions:
For problem 22, $x = 4$ . For problem 25, $x = 5$ . For problem 28, $x = 6$ .

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Solve for $x$ in the following linear equations: $x+x+x+3=15$ , $6x+11+5x=66$ , $6x-3=4x+9$ .

STEP 1

Assumptions
1. We are solving linear equations with one variable, $x$ .
2. The goal is to isolate $x$ on one side of the equation to find its value.
Problem 22: $x + x + x + 3 = 15$

STEP 2

Combine like terms on the left side of the equation.
$3x + 3 = 15$

STEP 3

Subtract 3 from both sides of the equation to isolate the term with $x$ .
$3x + 3 - 3 = 15 - 3$

STEP 4

Simplify both sides of the equation.
$3x = 12$

STEP 5

Divide both sides of the equation by 3 to solve for $x$ .
$\frac{3x}{3} = \frac{12}{3}$

STEP 6

Calculate the value of $x$ .
$x = 4$
Problem 25: $6x + 11 + 5x = 66$

STEP 7

Combine like terms on the left side of the equation.
$11x + 11 = 66$

STEP 8

Subtract 11 from both sides of the equation to isolate the term with $x$ .
$11x + 11 - 11 = 66 - 11$

STEP 9

Simplify both sides of the equation.
$11x = 55$

STEP 10

Divide both sides of the equation by 11 to solve for $x$ .
$\frac{11x}{11} = \frac{55}{11}$

STEP 11

Calculate the value of $x$ .
$x = 5$
Problem 28: $6x - 3 = 4x + 9$

STEP 12

Subtract $4x$ from both sides of the equation to get all terms with $x$ on one side.
$6x - 4x - 3 = 4x - 4x + 9$

STEP 13

Simplify both sides of the equation.
$2x - 3 = 9$

STEP 14

Add 3 to both sides of the equation to isolate the term with $x$ .
$2x - 3 + 3 = 9 + 3$

STEP 15

Simplify both sides of the equation.
$2x = 12$

STEP 16

Divide both sides of the equation by 2 to solve for $x$ .
$\frac{2x}{2} = \frac{12}{2}$

STEP 17

Calculate the value of $x$ .
$x = 6$
Solutions:
For problem 22, $x = 4$ . For problem 25, $x = 5$ . For problem 28, $x = 6$ .

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Solve for xxx in the following linear equations: x+x+x+3=15x+x+x+3=15x+x+x+3=15, 6x+11+5x=666x+11+5x=666x+11+5x=66, 6x−3=4x+96x-3=4x+96x−3=4x+9.

STEP 1

Assumptions1. We are solving linear equations with one variable, xxx.2. The goal is to isolate xxx on one side of the equation to find its value.Problem 22: x+x+x+3=15x + x + x + 3 = 15x+x+x+3=15

STEP 2

Combine like terms on the left side of the equation.3x+3=153x + 3 = 153x+3=15

STEP 3

Subtract 3 from both sides of the equation to isolate the term with xxx.3x+3−3=15−33x + 3 - 3 = 15 - 33x+3−3=15−3

STEP 4

Simplify both sides of the equation.3x=123x = 123x=12

STEP 5

Divide both sides of the equation by 3 to solve for xxx.3x3=123\frac{3x}{3} = \frac{12}{3}33x​=312​

STEP 6

Calculate the value of xxx.x=4x = 4x=4Problem 25: 6x+11+5x=666x + 11 + 5x = 666x+11+5x=66

STEP 7

Combine like terms on the left side of the equation.11x+11=6611x + 11 = 6611x+11=66

STEP 8

Subtract 11 from both sides of the equation to isolate the term with xxx.11x+11−11=66−1111x + 11 - 11 = 66 - 1111x+11−11=66−11

STEP 9

Simplify both sides of the equation.11x=5511x = 5511x=55

STEP 10

Divide both sides of the equation by 11 to solve for xxx.11x11=5511\frac{11x}{11} = \frac{55}{11}1111x​=1155​

STEP 11

Calculate the value of xxx.x=5x = 5x=5Problem 28: 6x−3=4x+96x - 3 = 4x + 96x−3=4x+9

STEP 12

Subtract 4x4x4x from both sides of the equation to get all terms with xxx on one side.6x−4x−3=4x−4x+96x - 4x - 3 = 4x - 4x + 96x−4x−3=4x−4x+9

STEP 13

Simplify both sides of the equation.2x−3=92x - 3 = 92x−3=9

STEP 14

Add 3 to both sides of the equation to isolate the term with xxx.2x−3+3=9+32x - 3 + 3 = 9 + 32x−3+3=9+3

STEP 15

Simplify both sides of the equation.2x=122x = 122x=12

STEP 16

Divide both sides of the equation by 2 to solve for xxx.2x2=122\frac{2x}{2} = \frac{12}{2}22x​=212​

STEP 17

Calculate the value of xxx.x=6x = 6x=6Solutions:For problem 22, x=4x = 4x=4. For problem 25, x=5x = 5x=5. For problem 28, x=6x = 6x=6.

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Solve for $x$ in the following linear equations: $x+x+x+3=15$ , $6x+11+5x=66$ , $6x-3=4x+9$ .

Assumptions
1. We are solving linear equations with one variable, $x$ .
2. The goal is to isolate $x$ on one side of the equation to find its value.
Problem 22: $x + x + x + 3 = 15$

Combine like terms on the left side of the equation.
$3x + 3 = 15$

Subtract 3 from both sides of the equation to isolate the term with $x$ .
$3x + 3 - 3 = 15 - 3$

Simplify both sides of the equation.
$3x = 12$

Divide both sides of the equation by 3 to solve for $x$ .
$\frac{3x}{3} = \frac{12}{3}$

Calculate the value of $x$ .
$x = 4$
Problem 25: $6x + 11 + 5x = 66$

Combine like terms on the left side of the equation.
$11x + 11 = 66$

Subtract 11 from both sides of the equation to isolate the term with $x$ .
$11x + 11 - 11 = 66 - 11$

Simplify both sides of the equation.
$11x = 55$

Divide both sides of the equation by 11 to solve for $x$ .
$\frac{11x}{11} = \frac{55}{11}$

Calculate the value of $x$ .
$x = 5$
Problem 28: $6x - 3 = 4x + 9$

Subtract $4x$ from both sides of the equation to get all terms with $x$ on one side.
$6x - 4x - 3 = 4x - 4x + 9$

Simplify both sides of the equation.
$2x - 3 = 9$

Add 3 to both sides of the equation to isolate the term with $x$ .
$2x - 3 + 3 = 9 + 3$

Simplify both sides of the equation.
$2x = 12$

Divide both sides of the equation by 2 to solve for $x$ .
$\frac{2x}{2} = \frac{12}{2}$

Calculate the value of $x$ .
$x = 6$
Solutions:
For problem 22, $x = 4$ . For problem 25, $x = 5$ . For problem 28, $x = 6$ .