Solve the Equations

142=58-7x
2x+96=-44-3x
-26=-7x+4(2x-4)
7x+5(-4x-4)=-124
-7x-35=28
10x+36=-108-2x

1. 7x = 58-142 = -84

X = -12.

2. 5x = -44-96 = -140
X = -28.

3. -26 = -7x+8x-16
-26 = x-16
x = 16-26 = -10

4. Similar to #3.

5. Similar to #1.

6.

To solve the equations, we will follow a step-by-step process to isolate the variable (x) and find its value.

1. 142 = 58 - 7x

To isolate the term with x, we will move the constant terms (numbers without x) to one side of the equation and the term with x to the other side.

→ 142 + 7x = 58

Now we will simplify the equation by combining like terms. Add 7x to both sides.

→ 142 + 7x + (-7x) = 58 + (-7x)

Simplifying further:

→ 142 = 58 + (-7x)

Next, we will move the constant term of 58 to the left side of the equation by subtracting it from both sides.

→ 142 - 58 = 58 + (-7x) - 58

Simplifying the equation:

→ 84 = -7x

Finally, to solve for x, we will divide both sides of the equation by -7.

→ 84 / -7 = -7x / -7

→ x = -12

Therefore, the solution to the equation is x = -12.

2. 2x + 96 = -44 - 3x

Following the same process, let's isolate the term with x.

→ 2x + 3x = -44 - 96

Combine like terms:

→ 5x = -140

To solve for x, divide both sides of the equation by 5:

→ 5x / 5 = -140 / 5

→ x = -28

So, the value of x is -28.

3. -26 = -7x + 4(2x - 4)

Start by simplifying the equation within parentheses:

→ -26 = -7x + 4(2x) + 4(-4)

→ -26 = -7x + 8x - 16

Combine like terms:

→ -26 = x - 16

Move the constant term -16 to the left side:

→ -26 + 16 = x

Simplify:

→ -10 = x

Therefore, x = -10.

4. 7x + 5(-4x - 4) = -124

To simplify the equation, distribute the 5 to both terms inside the parentheses:

→ 7x - 20x - 20 = -124

Combine like terms:

→ -13x - 20 = -124

Move the constant term -20 to the right side:

→ -13x = -124 + 20

Simplify:

→ -13x = -104

To solve for x, divide both sides of the equation by -13:

→ -13x / -13 = -104 / -13

→ x = 8

Therefore, the solution is x = 8.

5. -7x - 35 = 28

To solve for x, isolate the term with x by moving the constant term -35 to the right side:

→ -7x = 28 + 35

Simplify:

→ -7x = 63

Divide both sides of the equation by -7 to solve for x:

→ -7x / -7 = 63 / -7

→ x = -9

The solution is x = -9.

6. 10x + 36 = -108 - 2x

First, add 2x to both sides to isolate the term with x:

→ 10x + 2x + 36 = -108

Combine like terms:

→ 12x + 36 = -108

Next, move the constant term 36 to the right side of the equation:

→ 12x = -108 - 36

Simplify:

→ 12x = -144

Divide both sides of the equation by 12:

→ 12x / 12 = -144 / 12

→ x = -12

Therefore, the solution is x = -12.