Question

Complete the equation so it has infinitely many solutions. $4x+7=4(x+3)–\_\_$

Answer 1

Completing the given linear equation:

The given equation is,

$4x+7=4(x+3)–\_\_$

For infinitely many solutions we have to reach the point where $x$ has no solution

Proceeding by assuming the missing term as $t$.

The equation becomes,

$$\begin{gathered} \Rightarrow 4x+7=4(x+3)–t....\left(i\right) \\ \Rightarrow 4x+7=4x+12–t \end{gathered}$$

Subtracting $7$ on both sides we get,

$$\begin{gathered} \Rightarrow 4x+7-7=4x+12–t-7 \\ \Rightarrow 4x=4x+5-t \end{gathered}$$

Finding value of $t$

Subtracting $4x$ on both sides of the above equation,

$$\begin{gathered} \Rightarrow 4x-4x=4x+5-t-4x \\ \Rightarrow 0=5-t \\ \Rightarrow t=5 \end{gathered}$$

So, for infinitely many solutions putting $t=5$ in equation $\left(i\right)$ we get,

$\Rightarrow 4x+7=4(x+3)–5$

Thus, the required equation is $\Rightarrow 4x+7=4(x+3)–5$.