Question

solve.

1. \\(8(x + 5) = 96\\)
2. \\(2 + 4(1 - 3a) = 42\\)
3. \\(4(1 - d) = 3(d - 1)\\)
4. \\(4(m + 5) = 2(m - 1)\\)

Explanation:

Solve Question 1

Using the Two-Step Equations and Algebraic Isolation knowledge points:
Divide both sides of \(8(x + 5) = 96\) by \(8\):

$$x + 5 = 12$$

Subtract \(5\) from both sides:

$$x = 7$$

Solve Question 2

Using the Combining Like Terms and Algebraic Isolation knowledge points:
Distribute the \(4\) in \(2 + 4(1 - 3a) = 42\):

$$2 + 4 - 12a = 42$$

Combine the constant terms:

$$6 - 12a = 42$$

Subtract \(6\) from both sides:

$$-12a = 36$$

Divide by \(-12\):

$$a = -3$$

Solve Question 3

Using the Variables on Both Sides and Combining Like Terms knowledge points:
Distribute on both sides of \(4(1 - d) = 3(d - 1)\):

$$4 - 4d = 3d - 3$$

Add \(4d\) to both sides:

$$4 = 7d - 3$$

Add \(3\) to both sides:

$$7 = 7d$$

Divide by \(7\):

$$d = 1$$

Solve Question 4

Using the Variables on Both Sides and Algebraic Isolation knowledge points:
Distribute on both sides of \(4(m + 5) = 2(m - 1)\):

$$4m + 20 = 2m - 2$$

Subtract \(2m\) from both sides:

$$2m + 20 = -2$$

Subtract \(20\) from both sides:

$$2m = -22$$

Divide by \(2\):

$$m = -11$$

Answer:

Question 1

\(x = 7\)

Question 2

\(a = -3\)

Question 3

\(d = 1\)

Question 4

\(m = -11\)