Question

The given equation is either linear or equivalent to a linear equation. Solve the equation.

$2\left(1-x\right)=3\left(1+2x\right)+5$

Short answer

The solution of the given equation is $x=-\frac{3}{4}$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$2\left(1-x\right)=3\left(1+2x\right)+5$

Step 3. Solve the given equation.

Simplify the given equation.

$\begin{array}{c}2\left(1\right)+2\left(-x\right)=3\left(1\right)+3\left(2x\right)+5\\ 2-2x=3+6x+5\end{array}$

Isolate variable terms.

$$\begin{gathered} -2x-6x=3+5-2 \\ -8x=6 \end{gathered}$$

Divide both sides by $-8$.

role="math" localid="1643307142631" $$\begin{gathered} \frac{-8x}{-8}=\frac{6}{-8} \\ x=-\frac{3}{4} \end{gathered}$$

Thus, the solution of the given equation is $x=-\frac{3}{4}$.