Question

question 11
solve and check the equation.
10(2x - 5) - 3 = 10(x - 4) + (7)
enter answer

question 12
determine the number by which both sides of the equation must be multiplied or divided, to obtain just x on the left side.
$\frac{2}{7}x = 6$; multiply by
a - $\frac{2}{7}$

Explanation:

Question 11

Step1: Expand both sides

$10(2x - 5)-3=20x-50 - 3=20x-53$ and $10(x - 4)+7=10x-40 + 7=10x-33$. 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: $10x-53 + 53=-33 + 53$, getting $10x=20$.

Step4: Solve for x

Divide both sides by 10: $x=\frac{20}{10}=2$.

Step5: Check the solution

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

To get just $x$ on the left - hand side of the equation $\frac{2}{7}x = 6$, we use the multiplicative inverse property. The coefficient of $x$ is $\frac{2}{7}$, and its multiplicative inverse is $\frac{7}{2}$. When we multiply both sides of the equation $\frac{2}{7}x = 6$ by $\frac{7}{2}$, we have $\frac{7}{2}\times\frac{2}{7}x=\frac{7}{2}\times6$. Since $\frac{7}{2}\times\frac{2}{7}=1$, we are left with $x$ on the left - hand side.

Answer:

$2$

Question 12