Question

problems 1–3: solve each equation. show your thinking.

1. $2(x + 5) = 3x + 1$
2. $3y - 4 = 6 - 2y$
3. $3(n + 2) = 9(6 - n)$

Explanation:

Step1: Expand left side of Eq1

$2x + 10 = 3x + 1$

Step2: Isolate $x$ terms (Eq1)

$10 - 1 = 3x - 2x$

Step3: Solve for $x$

$x = 9$

Step1: Isolate $y$ terms (Eq2)

$3y + 2y = 6 + 4$

Step2: Combine like terms (Eq2)

$5y = 10$

Step3: Solve for $y$

$y = \frac{10}{5} = 2$

Step1: Expand both sides of Eq3

$3n + 6 = 54 - 9n$

Step2: Isolate $n$ terms (Eq3)

$3n + 9n = 54 - 6$

Step3: Combine like terms (Eq3)

$12n = 48$

Step4: Solve for $n$

$n = \frac{48}{12} = 4$

Answer:

1. $x = 9$
2. $y = 2$
3. $n = 4$