Question

Solve the equation 5x-7=3x+2

Answer 1

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

$\sf 5x-7=3x+2$

Step 1: Subtract 3x from both sides.

$\sf 5x-7-3x=3x+2-3x$

$\sf 2x-7=2$

Step 2: Add 7 to both sides.

$\sf 2x-7+7=2+7$

$\sf 2x = 9$

Step 3: Divide both sides by 2.

$\sf \frac{2x}{2}=\frac{9}{2}$

$\sf x = \frac{9}{2}$

Verification if $\sf \bf x = \frac{9}{2}$

⇒ $\sf 5x-7=3x+2$

⇒ $\sf ( 5\times \frac{9}{2}) -7=(3\times \frac{9}{2} )+2$

⇒ $\sf \frac{45}{2} -7=\frac{27}{2} +2$

⇒ $\sf \frac{45}{2 } -\frac{7\times 2 }{1\times 2 } =\frac{27}{2} +\frac{2\times 2 }{1\times 2 }$

⇒ $\sf \frac{45}{2 } -\frac{14 }{ 2 } =\frac{27}{2} +\frac{4}{2 }$

⇒ $\sf \frac{31}{2} = \frac{31}{2}$

$\sf \bf \therefore \ x = \frac{9}{2} \ in \ the \ equation \ => \ 5x-7=3x+2$

Additional Information :)

Let's start with an example.

5 added to a number gives us 17. Find the number.

We know it's 12 but that's not why I asked this question. I want to know how can we represent this in a simpler way. We can probably say ⇒ $\sf x+5=17$, find 'x'. This is called as an equation and it helps us to write number statements in a simpler way.

This equation only has one variable and it is unknown. These types of equations are known as Linear Equations in one variable which is also known as First Degree Equations in one Variable. They are known as Linear of First Degree because the highest power of the variable is 1.

An equation consists of three main parts. They are listed below.

• LHS (Left Hand Side)
• RHS (Right Hand Side)
• Equal Sign.