Question

equation|acceptable moves (steps)|work to find solution|check
-8 = 4(m + 7)|-8 = 4(m + 7)
2x + 10 = 4x - 6
12a - 3 = 5a - 24
57 = 8 + 4(y + 5)

Explanation:

Step1: Solve -8 = 4(m + 7)

First, divide both sides by 4.
$$-8\div4=4(m + 7)\div4$$
$$-2=m + 7$$
Then subtract 7 from both sides.
$$-2-7=m+7 - 7$$
$$m=-9$$

Check:

Substitute m = - 9 into the original equation:
Left - hand side: - 8
Right - hand side: $4(-9 + 7)=4\times(-2)=-8$

Step2: Solve 2x + 10 = 4x - 6

Subtract 2x from both sides.
$$2x+10-2x=4x - 6-2x$$
$$10 = 2x-6$$
Add 6 to both sides.
$$10 + 6=2x-6 + 6$$
$$16=2x$$
Divide both sides by 2.
$$x = 8$$

Check:

Left - hand side: $2\times8+10=16 + 10=26$
Right - hand side: $4\times8-6=32-6=26$

Step3: Solve 12a - 3 = 5a - 24

Subtract 5a from both sides.
$$12a-3-5a=5a - 24-5a$$
$$7a-3=-24$$
Add 3 to both sides.
$$7a-3 + 3=-24 + 3$$
$$7a=-21$$
Divide both sides by 7.
$$a=-3$$

Check:

Left - hand side: $12\times(-3)-3=-36-3=-39$
Right - hand side: $5\times(-3)-24=-15-24=-39$

Step4: Solve 57 = 8+4(y + 5)

First, distribute the 4.
$$57=8 + 4y+20$$
Combine like terms.
$$57=4y + 28$$
Subtract 28 from both sides.
$$57-28=4y+28 - 28$$
$$29=4y$$
Divide both sides by 4.
$$y=\frac{29}{4}=7.25$$

Check:

Right - hand side: $8+4(7.25 + 5)=8+4\times12.25=8 + 49=57$

Answer:

For -8 = 4(m + 7), m=-9; for 2x + 10 = 4x - 6, x = 8; for 12a - 3 = 5a - 24, a=-3; for 57 = 8+4(y + 5), y = 7.25