Final answer:
Gabe's next step in solving the equation 3(x-2) + 4 = 2x - 1 is to distribute the 3 into the parenthesis and then rearrange the equation to isolate the variable x. After combining like terms and moving terms to their respective sides, Gabe should end with a simplified equation. Finally, Gabe must check that the solution is reasonable by plugging the value of x back into the original equation.
Step-by-step explanation:
In the equation 3(x-2) + 4 = 2x - 1, Gabe's next step in solving the equation should be to distribute the 3 into the parenthesis and to rearrange the equation to isolate the variable x. The equation includes only one unknown, which simplifies the process of solving it. To distribute, Gabe would multiply 3 by both x and -2, resulting in 3x - 6. After distributing, the equation becomes 3x - 6 + 4 = 2x - 1. Gabe can then continue by combining like terms and moving the variable terms to one side of the equation and the constant terms to the other.
Here's a step-by-step reorder to solve the equation:
- Distribute the 3 to both x and -2, making the equation 3x - 6 + 4.
- Combine the constant terms on the left side: 3x - 6 + 4 becomes 3x - 2.
- Move the variable term 2x from the right to the left side by subtracting 2x from both sides, resulting in 3x - 2x = -1 + 2.
- Simplify both sides: x = 1.
Once Gabe has the simplified equation, he should then check the answer to ensure it is reasonable and correct by substituting x back into the original equation.