Question

question 2
0.42 points
solve and check the equation.
10(2x - 5) - 3 = 10(x - 4) + (7)
enter answer

Explanation:

Step1: Expand both sides

Expand \(10(2x - 5)-3\) to get \(20x-50 - 3=20x-53\), and expand \(10(x - 4)+7\) to get \(10x-40 + 7=10x-33\). So the equation becomes \(20x-53 = 10x-33\).

Step2: Move terms with \(x\) to one - side

Subtract \(10x\) from both sides: \(20x-10x-53=10x-10x - 33\), which simplifies to \(10x-53=-33\).

Step3: Isolate the term with \(x\)

Add 53 to both sides: \(10x-53 + 53=-33 + 53\), resulting in \(10x = 20\).

Step4: Solve for \(x\)

Divide both sides by 10: \(\frac{10x}{10}=\frac{20}{10}\), so \(x = 2\).

Step5: Check the solution

Substitute \(x = 2\) into the original equation.
Left - hand side: \(10(2\times2-5)-3=10(4 - 5)-3=10\times(-1)-3=-10 - 3=-13\).
Right - hand side: \(10(2 - 4)+7=10\times(-2)+7=-20 + 7=-13\).
Since the left - hand side equals the right - hand side when \(x = 2\), the solution is correct.

Answer:

\(x = 2\)