Question

Write an algebraic equation for each problem and then solve the equation.

Twice a number increased by 7 is equal to 4 times the same number decreased by 11.
a) 2x + 7 = 4x - 11
b) 2x - 7 = 4x + 11
c) 2x - 7 = 4x - 11
d) 2x + 7 = 4x + 11

Answer 1

The correct algebraic equation is 2x + 7 = 4x - 11, which simplifies when solved to x = 9. The solution is verified by substituting it back into the original equation, affirming that the answer is reasonable.

Step-by-step explanation:

The correct answer is option a) 2x + 7 = 4x - 11. To solve the algebraic equation, we perform the following steps:

1. Subtract 2x from both sides: 2x + 7 - 2x = 4x - 11 - 2x, which simplifies to 7 = 2x - 11.
2. Add 11 to both sides: 7 + 11 = 2x, which simplifies to 18 = 2x.
3. Divide both sides by 2 to solve for x: 18 / 2 = 2x / 2, which gives us x = 9.

After solving, we check that the answer is reasonable by substituting x back into the original equation: 2(9) + 7 = 4(9) - 11, which results in 18 + 7 = 36 - 11, confirming that 25 = 25. Therefore, our answer x = 9 is correct.

To solve the equation, we need to isolate the variable x on one side of the equation by performing the same operation on both sides. We start by subtracting 2x from both sides, which gives us:

7 = 2x - 11

Next, we add 11 to both sides to cancel out the -11, which gives us:

18 = 2x

Finally, we divide both sides by 2 to solve for x:

x = 9

To check our answer, we substitute x = 9 back into the original equation:

2(9) + 7 = 4(9) - 11

18 + 7 = 36 - 11

25 = 25

Since both sides of the equation are equal, our solution is correct.