Math  /  Algebra

QuestionUnit 1: Geometry Assignments 1.1 Name: \qquad ALGEBRA REVIEW Solve each equation for the indicated variable. The correct solution to each problem should show up once in the solution bank.  1. x+3=5\text { 1. } x+3=5
2. x4=11x-4=11
3. 13x=6\frac{1}{3} x=6
4. 2x=122 x=12
5. 2x11=1052 x-11=105
6. 34x11=22\frac{3}{4} x-11=22
7. 3x+2=113 x+2=11
8. 3x+8+2x5=233 x+8+2 x-5=23
9. 3x+8=2x+133 x+8=2 x+13

Solution Bank: 5215581846443\begin{array}{lllllllll}5 & 2 & 15 & 58 & 18 & 4 & 6 & 44 & 3\end{array}
Solving Equations with Variables on Both Sides and Fractions
10. 5+12x=31-5+12 x=31
11. 9x+18+3x=909 x+18+3 x=90
12. 4y+110=34 y+1-10=3
13. 3x+5x=243 x+5 x=24
14. 10x+1=18010 x+1=180
15. x+13=2x+2x+13=2 x+2

Studdy Solution

STEP 1

1. Each equation provided involves basic algebraic operations.
2. The goal is to isolate the indicated variable (usually xx or yy) on one side of the equation to find its value.
3. The solution should match one of the answers provided in the solution bank.

STEP 2

1. Solve simple linear equations.
2. Solve linear equations involving fractions.
3. Solve linear equations with variables on both sides.
4. Validate each solution with the solution bank.

STEP 3

Solve the equation x+3=5x + 3 = 5 for xx.
x+3=5x + 3 = 5 Subtract 3 from both sides: x=53x = 5 - 3 x=2x = 2

STEP 4

Solve the equation x4=11x - 4 = 11 for xx.
x4=11x - 4 = 11 Add 4 to both sides: x=11+4x = 11 + 4 x=15x = 15

STEP 5

Solve the equation 13x=6\frac{1}{3}x = 6 for xx.
13x=6\frac{1}{3}x = 6 Multiply both sides by 3: x=6×3x = 6 \times 3 x=18x = 18

STEP 6

Solve the equation 2x=122x = 12 for xx.
2x=122x = 12 Divide both sides by 2: x=122x = \frac{12}{2} x=6x = 6

STEP 7

Solve the equation 2x11=1052x - 11 = 105 for xx.
2x11=1052x - 11 = 105 Add 11 to both sides: 2x=105+112x = 105 + 11 2x=1162x = 116 Divide both sides by 2: x=1162x = \frac{116}{2} x=58x = 58

STEP 8

Solve the equation 34x11=22\frac{3}{4}x - 11 = 22 for xx.
34x11=22\frac{3}{4}x - 11 = 22 Add 11 to both sides: 34x=22+11\frac{3}{4}x = 22 + 11 34x=33\frac{3}{4}x = 33 Multiply both sides by 43\frac{4}{3}: x=33×43x = 33 \times \frac{4}{3} x=44x = 44

STEP 9

Solve the equation 3x+2=113x + 2 = 11 for xx.
3x+2=113x + 2 = 11 Subtract 2 from both sides: 3x=1123x = 11 - 2 3x=93x = 9 Divide both sides by 3: x=93x = \frac{9}{3} x=3x = 3

STEP 10

Solve the equation 3x+8+2x5=233x + 8 + 2x - 5 = 23 for xx.
Combine like terms: 5x+3=235x + 3 = 23 Subtract 3 from both sides: 5x=2335x = 23 - 3 5x=205x = 20 Divide both sides by 5: x=205x = \frac{20}{5} x=4x = 4

STEP 11

Solve the equation 3x+8=2x+133x + 8 = 2x + 13 for xx.
Subtract 2x2x from both sides: x+8=13x + 8 = 13 Subtract 8 from both sides: x=138x = 13 - 8 x=5x = 5

STEP 12

Solve the equation 5+12x=31-5 + 12x = 31 for xx.
Add 5 to both sides: 12x=31+512x = 31 + 5 12x=3612x = 36 Divide both sides by 12: x=3612x = \frac{36}{12} x=3x = 3

STEP 13

Solve the equation 9x+18+3x=909x + 18 + 3x = 90 for xx.
Combine like terms: 12x+18=9012x + 18 = 90 Subtract 18 from both sides: 12x=901812x = 90 - 18 12x=7212x = 72 Divide both sides by 12: x=7212x = \frac{72}{12} x=6x = 6

STEP 14

Solve the equation 4y+110=34y + 1 - 10 = 3 for yy.
Combine like terms: 4y9=34y - 9 = 3 Add 9 to both sides: 4y=3+94y = 3 + 9 4y=124y = 12 Divide both sides by 4: y=124y = \frac{12}{4} y=3y = 3

STEP 15

Solve the equation 3x+5x=243x + 5x = 24 for xx.
Combine like terms: 8x=248x = 24 Divide both sides by 8: x=248x = \frac{24}{8} x=3x = 3

STEP 16

Solve the equation 10x+1=18010x + 1 = 180 for xx.
Subtract 1 from both sides: 10x=180110x = 180 - 1 10x=17910x = 179 Divide both sides by 10: x=17910x = \frac{179}{10} x=17.9x = 17.9

STEP 17

Solve the equation x+13=2x+2x + 13 = 2x + 2 for xx.
Subtract xx from both sides: 13=x+213 = x + 2 Subtract 2 from both sides: x=132x = 13 - 2 x=11x = 11

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