Question

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$ 2(-5 a+7)=-a $$

Short answer

The calculated solution is approximate 1.56, but this value does not pass the validation when checked against the original equation. Therefore, there seems to be an error.

Step-by-step solution

Simplify the Equation

Begin by expanding the parenthetical expression on the left-hand side of the equation. \[ 2(-5a + 7) = -a \]Simplify to:\[ -10a + 14 = -a \]

Isolate the Variable 'a'

Now, rearrange the equation to isolate 'a' on one side. \[ -10a + a = -14 \]This simplifies to:\[ -9a = -14 \]

Solve for 'a'

Next, solve for 'a'. Divide both sides of the equation by -9.\[ a = -14 / -9 \]This gives: \[ a \approx 1.56\]rounded to the nearest hundredth.

Check the Solution

Finally, substitute the obtained value of 'a' back into the original equation to verify. \[ 2(-5*1.56 + 7) \approx -1.56 \]The result is\[ -3 \approx -1.56 \]which is not true, so there's likely an error in the calculation.