Question

directions: solve the following equations below. remember to show your work!
problem 11: (3(x - 15)=x + 11); problem 12: (-4y - 10 = 4(y - 3)); problem 13: (2(3d + 3)=7 + 6d); problem 14: (-5(4 - 3n)=10(n - 2))

Explanation:

Problem 11

Step1: Expand left side

$3x - 45 = x + 11$

Step2: Isolate x terms

$3x - x = 11 + 45$

Step3: Simplify both sides

$2x = 56$

Step4: Solve for x

$x = \frac{56}{2} = 28$

Problem 12

Step1: Expand right side

$-4y - 10 = 4y - 12$

Step2: Isolate y terms

$-4y - 4y = -12 + 10$

Step3: Simplify both sides

$-8y = -2$

Step4: Solve for y

$y = \frac{-2}{-8} = \frac{1}{4}$

Problem 13

Step1: Expand left side

$6d + 6 = 7 + 6d$

Step2: Isolate d terms

$6d - 6d = 7 - 6$

Step3: Simplify both sides

$0 = 1$

Problem 14

Step1: Expand both sides

$-20 + 15n = 10n - 20$

Step2: Isolate n terms

$15n - 10n = -20 + 20$

Step3: Simplify both sides

$5n = 0$

Step4: Solve for n

$n = \frac{0}{5} = 0$

Answer:

Problem 11: $x = 28$
Problem 12: $y = \frac{1}{4}$
Problem 13: No solution (since $0=1$ is false)
Problem 14: $n = 0$