Question

4(x+2)/5=7+5x/13

Can anyone please give me the step by step explanation of the above equation asap? ​

Answer 1

$\huge { \underline\red {\bf{Solution}}}$

Let's solve your equation step-by-step.

$\bf{ \frac{4(x + 2)}{5} \: = \: 7 \: + \: \frac{5x}{13} }$

Step 1: Simplify both sides of the equation.

$\bf{\frac{4(x + 2)}{5} \: = \: 7 \: + \: \frac{5x}{13} }$

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: = \: 7 \: + \: \frac{5x}{13} \: \: \: (Distribute)}$

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: = \: 7 \: + \: \frac{5}{13}x}$

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: = \: \frac{5}{13}x \: + \: 7}$

Step 2: Subtract $\bf\frac{5}{13}x$ from both sides.

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: - \: \blue{ \frac{5}{13}x} \: = \: \frac{5}{13}x \: + \: 7}\: - \: \blue{ \frac{5}{13}x}$

$\bf{ \frac{27}{65}x \: + \: \frac{8}{5} \: = \: 7}$

Step 3: Subtract $\bf\frac{8}{5}$ from both sides.

$\bf{\frac{27}{65}x \: + \: \frac{8}{5} \: - \: \blue{ \frac{8}{5} } \: = \: 7\: - \: \blue{ \frac{8}{5} }}$

$\bf{ \frac{27}{65}x \: = \: \frac{27}{5} }$

Step 4: Multiply both sides by $\bf\frac{65}{27}$.

${\big(\frac \blue{65} \blue{27} \big) \:* \: \big( \frac{27}{65}x \big) \: = \: \big(\frac \blue{65} \blue{27} \big) \: * \: \big( \frac{27}{5} \big) }$

$\bf{x \: = \: 13}$

$\huge { \underline\red {\bf{Answer}}}$

$\bf{x \: = \: 13}$

Answer 2

Answer:

$[tex] \huge { \underline\red {\bf{Solution}}}$

Let's solve your equation step-by-step.

$\bf{ \frac{4(x + 2)}{5} \: = \: 7 \: + \: \frac{5x}{13} }$

Step 1: Simplify both sides of the equation.

$\bf{\frac{4(x + 2)}{5} \: = \: 7 \: + \: \frac{5x}{13} }$

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: = \: 7 \: + \: \frac{5x}{13} \: \: \: (Distribute)}$

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: = \: 7 \: + \: \frac{5}{13}x}$

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: = \: \frac{5}{13}x \: + \: 7}$

Step 2: Subtract $\bf\frac{5}{13}x$ from both sides.

$\bf{\frac{4}{5}x \: + \: \frac{8}{5} \: - \: \blue{ \frac{5}{13}x} \: = \: \frac{5}{13}x \: + \: 7}\: - \: \blue{ \frac{5}{13}x}$

$\bf{ \frac{27}{65}x \: + \: \frac{8}{5} \: = \: 7}$

Step 3: Subtract $\bf\frac{8}{5}$ from both sides.

$\bf{\frac{27}{65}x \: + \: \frac{8}{5} \: - \: \blue{ \frac{8}{5} } \: = \: 7\: - \: \blue{ \frac{8}{5} }}$

$\bf{ \frac{27}{65}x \: = \: \frac{27}{5} }$

Step 4: Multiply both sides by $\bf\frac{65}{27}$.

${\big(\frac \blue{65} \blue{27} \big) \:* \: \big( \frac{27}{65}x \big) \: = \: \big(\frac \blue{65} \blue{27} \big) \: * \: \big( \frac{27}{5} \big) }$

$\bf{x \: = \: 13}$

$\huge { \underline\red {\bf{Answer}}}$

$\bf{x \: = \: 13}$[/tex]