16(3x – 5) – 10(4x – 8) = 40. Please solve and verify as soon as possible.
The Correct Answer and Explanation is:
Let’s solve the equation:16(3x−5)−10(4x−8)=4016(3x – 5) – 10(4x – 8) = 4016(3x−5)−10(4x−8)=40
Step 1: Distribute the constants
Distribute 16 into 3x−53x – 53x−5:16(3x−5)=48x−8016(3x – 5) = 48x – 8016(3x−5)=48x−80
Distribute -10 into 4x−84x – 84x−8:−10(4x−8)=−40x+80-10(4x – 8) = -40x + 80−10(4x−8)=−40x+80
Now substitute back into the equation:48x−80−40x+80=4048x – 80 – 40x + 80 = 4048x−80−40x+80=40
Step 2: Combine like terms
Combine 48x48x48x and −40x-40x−40x:(48x−40x)=8x(48x – 40x) = 8x(48x−40x)=8x
Combine −80-80−80 and +80+80+80:−80+80=0-80 + 80 = 0−80+80=0
So the equation becomes:8x=408x = 408x=40
Step 3: Solve for xxx
x=408=5x = \frac{40}{8} = 5x=840=5
Step 4: Verify the solution
Plug x=5x = 5x=5 back into the original equation:16(3(5)−5)−10(4(5)−8)=4016(3(5) – 5) – 10(4(5) – 8) = 4016(3(5)−5)−10(4(5)−8)=40
Simplify inside the parentheses:16(15−5)−10(20−8)=4016(15 – 5) – 10(20 – 8) = 4016(15−5)−10(20−8)=4016(10)−10(12)=4016(10) – 10(12) = 4016(10)−10(12)=40160−120=40160 – 120 = 40160−120=40
✅ Verified: Left side = Right side = 40
Explanation
To solve the equation 16(3x−5)−10(4x−8)=4016(3x – 5) – 10(4x – 8) = 4016(3x−5)−10(4x−8)=40, we follow a step-by-step algebraic process. This equation involves distributing constants across parentheses and simplifying. The first step is to apply the distributive property. We multiply 16 by both terms inside the first parentheses, resulting in 48x−8048x – 8048x−80. Then, we multiply -10 by the terms in the second parentheses. Note that the negative sign must be applied to the entire expression, giving −40x+80-40x + 80−40x+80.
After distributing, the equation becomes 48x−80−40x+80=4048x – 80 – 40x + 80 = 4048x−80−40x+80=40. Combining like terms simplifies this to 8x=408x = 408x=40. To isolate xxx, we divide both sides by 8, resulting in x=5x = 5x=5.
Verification is crucial. By substituting x=5x = 5x=5 into the original equation, we evaluate both sides and confirm they are equal. Plugging in, we compute:
16(15−5)−10(20−8)=160−120=4016(15 – 5) – 10(20 – 8) = 160 – 120 = 4016(15−5)−10(20−8)=160−120=40, which matches the right side of the equation. This confirms the solution is correct.
This process illustrates core algebra principles: distribution, combining like terms, and solving linear equations. It’s essential to apply each step methodically and verify the solution to ensure accuracy. By practicing these steps, you build confidence in solving increasingly complex algebraic equations.
