Question

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Solve: $\sqrt{7y+1}=\sqrt{2y-5}$

Short answer

Ans:$\sqrt{7y+1}=\sqrt{2y-5}\Rightarrow y=-\frac{6}{5}(Decimal:y=-1.2)$

Step-by-step solution

Step 1. Given information.

given expression: $\sqrt{7y+1}=\sqrt{2y-5}$

Step 2. Square both sides of the equation. 

$$\begin{gathered} {(\sqrt{7y+1})}^2={\left(\sqrt{2y-5}\right)}^2 \\ \Rightarrow 7y+1=2y-5 \end{gathered}$$

Step 3. Simplify, then the new equation. 

$$\begin{gathered} 7y+1=2y-5 \\ \Rightarrow 5y=-6 \\ \Rightarrow y=-\frac{6}{5}=-1.2 \end{gathered}$$

Therefore, the value of$y=-\frac{6}{5}or-1.2$

Check the answer.

$$\begin{gathered} \sqrt{7y+1}=\sqrt{2y-5} \\ \Rightarrow \sqrt{7\times -1.2+1}=\sqrt{2\times -1.2-5} \\ \Rightarrow \sqrt{-7.4}=\sqrt{-7.4} \end{gathered}$$

The solution islocalid="1647893287374" $y=-\frac{6}{5}=-1.2$