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Math  /  Algebra

Question7) 6x−32=2x−5\frac{6 x-3}{2}=2 x-5

Studdy Solution

STEP 1

1. The equation 6x−32=2x−5\frac{6x-3}{2} = 2x - 5 is a linear equation.
2. The goal is to solve for the variable x x .
3. Basic algebraic operations such as multiplication, addition, and subtraction will be used.

STEP 2

1. Eliminate the fraction by multiplying both sides by the denominator.
2. Simplify and rearrange the equation to isolate terms involving x x .
3. Solve for x x by isolating it on one side of the equation.
4. Check the solution by substituting it back into the original equation.

STEP 3

Multiply both sides of the equation by 2 to eliminate the fraction:
2×6x−32=2×(2x−5) 2 \times \frac{6x - 3}{2} = 2 \times (2x - 5)
This simplifies to:
6x−3=4x−10 6x - 3 = 4x - 10

STEP 4

Rearrange the equation to get all terms involving x x on one side and constant terms on the other side. Subtract 4x 4x from both sides:
6x−4x−3=−10 6x - 4x - 3 = -10
This simplifies to:
2x−3=−10 2x - 3 = -10

STEP 5

Add 3 to both sides to isolate the term with x x :
2x−3+3=−10+3 2x - 3 + 3 = -10 + 3
This simplifies to:
2x=−7 2x = -7
Now, divide both sides by 2 to solve for x x :
x=−72 x = \frac{-7}{2}

STEP 6

Check the solution by substituting x=−72 x = \frac{-7}{2} back into the original equation:
Original equation: 6x−32=2x−5\frac{6x - 3}{2} = 2x - 5
Substitute x=−72 x = \frac{-7}{2} :
6(−72)−32=2(−72)−5 \frac{6\left(\frac{-7}{2}\right) - 3}{2} = 2\left(\frac{-7}{2}\right) - 5
Simplify both sides:
Left side: −21−32=−242=−12\frac{-21 - 3}{2} = \frac{-24}{2} = -12
Right side: −7−5=−12-7 - 5 = -12
Both sides are equal, confirming the solution is correct.
The solution is:
−72 \boxed{\frac{-7}{2}}

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