Question

10x - 36 - 2x = -4(x - 15)
10x - 2x - 36 = -4(x - 15)
8x - 36 = -4(x - 15)
8x - 36 = -4x + 60
12x - 36 = 60
12x = 96
x = 8

Explanation:

To solve these equations, we'll go through each one step by step:

1. Solve \(10x - 36 - 2x = -4(x - 15)\)

Step 1: Simplify both sides

Simplify the left side: \(10x - 2x - 36 = 8x - 36\)
Simplify the right side: \(-4(x - 15) = -4x + 60\) (using the distributive property \(a(b - c) = ab - ac\))
So the equation becomes: \(8x - 36 = -4x + 60\)

Step 2: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 3: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 4: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

2. Let's verify the solution \(x = 8\) in the original equation \(10x - 36 - 2x = -4(x - 15)\)

Step 1: Substitute \(x = 8\) into the left side

Left side: \(10(8) - 36 - 2(8) = 80 - 36 - 16 = 28\)

Step 2: Substitute \(x = 8\) into the right side

Right side: \(-4(8 - 15) = -4(-7) = 28\)

Since the left side equals the right side when \(x = 8\), the solution is correct.

For the other equations (they are just intermediate steps in the process of solving the first equation, but if we were to solve them individually):

Equation: \(12x = 96\)

Step 1: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(12x - 36 = 60\)

Step 1: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 2: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(8x - 36 = -4x + 60\)

Step 1: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 2: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 3: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(8x - 36 = -4(x - 15)\)

Step 1: Simplify the right side

\(-4(x - 15) = -4x + 60\)

Step 2: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 3: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 4: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(10x - 2x - 36 = -4(x - 15)\)

Step 1: Simplify the left side

\(8x - 36 = -4(x - 15)\)

Step 2: Simplify the right side

\(-4(x - 15) = -4x + 60\)

Step 3: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 4: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 5: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Final Answer

For all the equations (the original and the intermediate ones), the solution is \(\boldsymbol{x = 8}\)

Answer:

To solve these equations, we'll go through each one step by step:

1. Solve \(10x - 36 - 2x = -4(x - 15)\)

Step 1: Simplify both sides

Simplify the left side: \(10x - 2x - 36 = 8x - 36\)
Simplify the right side: \(-4(x - 15) = -4x + 60\) (using the distributive property \(a(b - c) = ab - ac\))
So the equation becomes: \(8x - 36 = -4x + 60\)

Step 2: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 3: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 4: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

2. Let's verify the solution \(x = 8\) in the original equation \(10x - 36 - 2x = -4(x - 15)\)

Step 1: Substitute \(x = 8\) into the left side

Left side: \(10(8) - 36 - 2(8) = 80 - 36 - 16 = 28\)

Step 2: Substitute \(x = 8\) into the right side

Right side: \(-4(8 - 15) = -4(-7) = 28\)

Since the left side equals the right side when \(x = 8\), the solution is correct.

For the other equations (they are just intermediate steps in the process of solving the first equation, but if we were to solve them individually):

Equation: \(12x = 96\)

Step 1: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(12x - 36 = 60\)

Step 1: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 2: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(8x - 36 = -4x + 60\)

Step 1: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 2: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 3: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(8x - 36 = -4(x - 15)\)

Step 1: Simplify the right side

\(-4(x - 15) = -4x + 60\)

Step 2: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 3: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 4: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Equation: \(10x - 2x - 36 = -4(x - 15)\)

Step 1: Simplify the left side

\(8x - 36 = -4(x - 15)\)

Step 2: Simplify the right side

\(-4(x - 15) = -4x + 60\)

Step 3: Add \(4x\) to both sides

\(8x + 4x - 36 = -4x + 4x + 60\)
\(12x - 36 = 60\)

Step 4: Add 36 to both sides

\(12x - 36 + 36 = 60 + 36\)
\(12x = 96\)

Step 5: Divide both sides by 12

\(\frac{12x}{12} = \frac{96}{12}\)
\(x = 8\)

Final Answer

For all the equations (the original and the intermediate ones), the solution is \(\boldsymbol{x = 8}\)