Question

Solve for x: 5(2x-1)=4(3x-2) ​

Answer 1

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

$5(2x-1)=4(3x-2)$

Step 1: Simplify both sides of the equation.

⇒ $5(2x-1)=4(3x-2)$

(Distribute)

⇒ $(5)(2x)+(5)(-1)=(4)(3x)+(4)(-2)$

⇒ $10x+-5=12x+-8$

⇒ $10x-5=12x-8$

Step 2: Subtract 12x from both sides.

⇒ $10x-5-12x=12x-8-12x$

⇒ $-2x-5=-8$

Step 3: Add 5 to both sides.

⇒ $-2x-5+5=-8+5$

⇒ $-2x=-3$

Step 4: Divide both sides by -2.

⇒ $\frac{-2x}{-2} =\frac{-3}{-2}$

⇒ $x=\frac{3}{2}$

Verification

⇒ $5(2x-1)=4(3x-2)$

⇒$5((2\times \frac{3}{2}) -1)=4((3\times \frac{3}{2}) -2)$

⇒ $5(3 -1)=4(\frac{9}{2} -2)$

⇒ $5(2)=4(\frac{9}{2} -\frac{2\times 2 }{1\times 2 } )$

⇒ $5(2)=4(\frac{9}{2} -\frac{4 }{2 } )$

⇒ $5(2)=4(\frac{5}{2} )$

⇒ $5\times 2=4\times \frac{5}{2}$

⇒ $5\times 2=(4\div 2) \times \frac{5}{2\div 2}$

⇒ $5\times 2=2 \times 5$

⇒ $10=10$

$\bf \therefore x=\frac{3}{2} \ in \ the \ equation =>\ 5(2x-1)=4(3x-2)$