Question

directions: solve each equation. check all solutions.

1. $7m + 29 = 2m + 9$
2. $10a - 7 = 7a - 55$
3. $-10k + 11 = 3 - 2k$
4. $6x - 16 = x + 29$
5. $3q - 19 = 10q + 23$
6. $38 - 6v = v + 24$

Explanation:

1. Equation: $7m + 29 = 2m + 9$

Step1: Isolate $m$ terms

$7m - 2m = 9 - 29$

Step2: Simplify both sides

$5m = -20$

Step3: Solve for $m$

$m = \frac{-20}{5} = -4$

Step4: Check solution

Left: $7(-4)+29=-28+29=1$; Right: $2(-4)+9=-8+9=1$

2. Equation: $10a - 7 = 7a - 55$

Step1: Isolate $a$ terms

$10a - 7a = -55 + 7$

Step2: Simplify both sides

$3a = -48$

Step3: Solve for $a$

$a = \frac{-48}{3} = -16$

Step4: Check solution

Left: $10(-16)-7=-160-7=-167$; Right: $7(-16)-55=-112-55=-167$

3. Equation: $-10k + 11 = 3 - 2k$

Step1: Isolate $k$ terms

$-10k + 2k = 3 - 11$

Step2: Simplify both sides

$-8k = -8$

Step3: Solve for $k$

$k = \frac{-8}{-8} = 1$

Step4: Check solution

Left: $-10(1)+11=-10+11=1$; Right: $3-2(1)=3-2=1$

4. Equation: $6x - 16 = x + 29$

Step1: Isolate $x$ terms

$6x - x = 29 + 16$

Step2: Simplify both sides

$5x = 45$

Step3: Solve for $x$

$x = \frac{45}{5} = 9$

Step4: Check solution

Left: $6(9)-16=54-16=38$; Right: $9+29=38$

5. Equation: $3q - 19 = 10q + 23$

Step1: Isolate $q$ terms

$3q - 10q = 23 + 19$

Step2: Simplify both sides

$-7q = 42$

Step3: Solve for $q$

$q = \frac{42}{-7} = -6$

Step4: Check solution

Left: $3(-6)-19=-18-19=-37$; Right: $10(-6)+23=-60+23=-37$

6. Equation: $38 - 6v = v + 24$

Step1: Isolate $v$ terms

$-6v - v = 24 - 38$

Step2: Simplify both sides

$-7v = -14$

Step3: Solve for $v$

$v = \frac{-14}{-7} = 2$

Step4: Check solution

Left: $38-6(2)=38-12=26$; Right: $2+24=26$

Answer:

$m=-4$
$a=-16$
$k=1$
$x=9$
$q=-6$
$v=2$