Question

solving equations with variables on both sides

1. move the like terms to one side of the equation.

like terms have the same variable raised to the same power

1. move the constants to the other side of the equation.
2. use properties of equality to solve the equation

$5x + 2 = 2x + 17$
$-2x$ $-2x$
$3x + 2 = 17$
$-2$ $-2$
$3x = 15$
$\div 3$ $\div 3$
$x=5$
solve each equation. show all of your work.
1 $3x + 7 = 8x - 5$
2 $4y + 10 = 2y + 22$
3 $6z - 3 = 9z + 12$
4 $7a + 14 = 3a - 6$
5 $5b - 15 = 8b + 10$
6 $3g - 12 = 7g + 14$
© to the square inch, 2023, www.tothesquareinc

Explanation:

Step1: Solve \( 3x + 7 = 8x - 5 \)

Subtract \( 3x \) from both sides: \( 7 = 5x - 5 \)
Add 5 to both sides: \( 12 = 5x \)
Divide by 5: \( x = \frac{12}{5} = 2.4 \)

Step2: Solve \( 4y + 10 = 2y + 22 \)

Subtract \( 2y \) from both sides: \( 2y + 10 = 22 \)
Subtract 10: \( 2y = 12 \)
Divide by 2: \( y = 6 \)

Step3: Solve \( 6z - 3 = 9z + 12 \)

Subtract \( 6z \): \( -3 = 3z + 12 \)
Subtract 12: \( -15 = 3z \)
Divide by 3: \( z = -5 \)

Step4: Solve \( 7a + 14 = 3a - 6 \)

Subtract \( 3a \): \( 4a + 14 = -6 \)
Subtract 14: \( 4a = -20 \)
Divide by 4: \( a = -5 \)

Step5: Solve \( 5b - 15 = 8b + 10 \)

Subtract \( 5b \): \( -15 = 3b + 10 \)
Subtract 10: \( -25 = 3b \)
Divide by 3: \( b = -\frac{25}{3} \approx -8.33 \)

Step6: Solve \( 3g - 12 = 7g + 14 \)

Subtract \( 3g \): \( -12 = 4g + 14 \)
Subtract 14: \( -26 = 4g \)
Divide by 4: \( g = -\frac{13}{2} = -6.5 \)

Answer:

1. \( x = \frac{12}{5} \)
2. \( y = 6 \)
3. \( z = -5 \)
4. \( a = -5 \)
5. \( b = -\frac{25}{3} \)
6. \( g = -\frac{13}{2} \)