Question

Solve the following equation $3x + 4 = 5(x - 2)$ .

Answer 1

Hint: In this question we have to solve the above equation . First we are going to solve the right hand side equation and then bring the x valued term of left hand side towards right , shift the numerical term of right hand side towards left . We can solve the rest. After getting the value of x we have to substitute the value of x in the above equation and need to verify that Left hand side = Right hand side ( L.H.S = R.H.S )

Complete step-by-step solution:
The given equation is $3x + 4 = 5(x - 2)$
$ 3x + 4 = 5(x - 2) \\
\Rightarrow 3x + 4 = 5x - 5 \times 2 \\
\Rightarrow 3x + 4 = 5x - 10 \\
\Rightarrow 4 = 5x - 10 - 3x \\
\Rightarrow 4 = 2x - 10 \\
\Rightarrow 4 + 10 = 2x \\
\Rightarrow 2x = 14 \\
\Rightarrow x = 7 \\$
Verification : Now substitute the value of x =7 in the equation $3x + 4 = 5(x - 2)$and verify L . H . S = R . H . S,
$ \Rightarrow 3 \times 7 + 4 = 5(7 - 2) \\
\Rightarrow 21 + 4 = 5 \times 5 \\
\Rightarrow 25 = 25 \\$
L.H.S=R.H.S
Therefore hence proved that the value of x=7 for equation $3x + 4 = 5(x - 2)$.

Note: The above given equation $3x + 4 = 5(x - 2)$ is a linear equation in a single variable. Solving the equation means getting the value of x . For solving equations like above we have to first simplify terms associated with parenthesis and brackets and then move forward for the variable associated terms .
Checking the terms of left hand side and right hand side assures us with a perfect , accurate and no error answer . As we are solving algebraic expressions and equations , verification ( L. H .S = R . H . S) is needed for getting correct answers .