Math

Question Solve for xx in the following linear equations: x+x+x+3=15x+x+x+3=15, 6x+11+5x=666x+11+5x=66, 6x3=4x+96x-3=4x+9.

Studdy Solution

STEP 1

Assumptions
1. We are solving linear equations with one variable, xx.
2. The goal is to isolate xx on one side of the equation to find its value.

Problem 22: x+x+x+3=15x + x + x + 3 = 15

STEP 2

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

STEP 3

Subtract 3 from both sides of the equation to isolate the term with xx.
3x+33=1533x + 3 - 3 = 15 - 3

STEP 4

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

STEP 5

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

STEP 6

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

STEP 7

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

STEP 8

Subtract 11 from both sides of the equation to isolate the term with xx.
11x+1111=661111x + 11 - 11 = 66 - 11

STEP 9

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

STEP 10

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

STEP 11

Calculate the value of xx.
x=5x = 5
Problem 28: 6x3=4x+96x - 3 = 4x + 9

STEP 12

Subtract 4x4x from both sides of the equation to get all terms with xx on one side.
6x4x3=4x4x+96x - 4x - 3 = 4x - 4x + 9

STEP 13

Simplify both sides of the equation.
2x3=92x - 3 = 9

STEP 14

Add 3 to both sides of the equation to isolate the term with xx.
2x3+3=9+32x - 3 + 3 = 9 + 3

STEP 15

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

STEP 16

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

STEP 17

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

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