Caleb solved this equation and recorded his work. 7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6 1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6 2. 15.6x − 16.4 = −2.3x + 35.4 3. 17.9x − 16.4 = 35.4 4. 17.9x = 51.8 5. x ≈ 2.89 When Caleb verified his solution, it didn’t work. What mistake did he make? In step 1, the distributive property was not used properly on the right side of the equation. In step 2, the like terms were not combined properly on the right side of the equation. In step 3, the addition property of equality was not used properly to isolate the variable term. In step 5, the division property of equality was not used properly to solve for x.
For this case we have the following equation: [tex]7.4x + 4.1 (2x - 4) = -2.3 (x - 6) - 21.6
[/tex] Step 1 of the solution is to make the distributive property. We have then: [tex]7.4x + 8.2x - 16.4 = -2.3x + 13.8 - 21.6
[/tex] Step 1 is correct. The step is to combine similar terms. Caleb wrote: [tex]7.4x + 8.2x - 16.4 = -2.3x + 35.4
[/tex] He wrongly combined the similar terms on the right side of the equation. The correct solution is: [tex] 7.4x + 8.2x - 16.4 = -2.3x -7.8
[/tex] Answer: In step 2, the like terms were not combined on the right side of the equation.
