Question

Solve each equation. Check your solution.

$-5\left(3-q\right)+4=5q-11$

Short answer

The given equation is an identity. Any value of $q$is a solution.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$-5\left(3-q\right)+4=5q-11$”.

Step 2. Solve the given equation.

Solving,

$-5\left(3-q\right)+4=5q-11$ (Given equation)

$-15+5q+4=5q-11$ (Distributive property)

$5q-11=5q-11$ (Simplify)

The expressions on both sides are identical.

This implies that the given equation is an identity. So, it is true for all values of $q$.

Step 3. Check the obtained solution.

Put $q=1$in the given equation $-5\left(3-q\right)+4=5q-11$to get,

$\begin{array}{l}-5\left(3-1\right)+4=5-11\\ -5\left(2\right)+4=-6\\ -10+4=-6\\ -6=-6\end{array}$

Since the values on the left-hand side and the right-hand side are equal, it can be said that $q=1$is a solution of the given equation.

Put $q=0$in the given equation $-5\left(3-q\right)+4=5q-11$to get,

$\begin{array}{l}-5\left(3-0\right)+4=5\left(0\right)-11\\ -5\left(3\right)+4=0-11\\ -15+4=-11\\ -11=-11\end{array}$

Since the values on the left-hand side and the right-hand side are equal, it can be said that $q=0$is a solution of the given equation.

Thus, it can be seen that a linear equation has at least two different solutions. This verifies that the given equation is an identity.