Question

-4(2x + 5) + 5x - 1 = - 48

Answer 1

$\tt x=9$

Step-by-step explanation:

$\tt -4(2x + 5) + 5x - 1 = - 48$

Apply the distributive property to multiply -4 by 2x+5:-

$\tt -8x-20+5x-1=-48$

Combine like terms:-

$\tt -3x-21=-48$

Add 21 to both sides:-

$\tt -3x=-48+21$

$\tt -3x=-27$

Divide both sides by -3:-

$\tt \: x = \cfrac{ - 27}{ - 3}$

$\tt x=9$

Hope this answers your question!

Answer 2

Answer:

x = 9

Step-by-step explanation:

Given equation:

$-4(2x + 5) + 5x - 1 = -48$

Apply distributive property rule: x(y + z) = xy + xz

$\implies -4(2x + 5) + 5x - 1 = -48$

$\implies (2x \times -4) + (4 \times 5) + 5x - 1 = -48$

$\implies -8x - 20 + 5x - 1 = -48$

Combine like terms on the left hand side to simplify the expression:

$\implies -8x - 20 + 5x - 1 = -48$

$\implies x(-8 + 5) + 1(-20 - 1) = -48$

$\implies x(-3) - 21 = -48$

Add 21 on both sides to remove all the mathematical operations (addition, subtraction, multiplication, division) being performed on the L.H.S

$\implies-3x + 21 - 21 = -48 + 21$

$\implies -3x = -27$

Cancel the "-" by dividing "-1" both sides:

$\implies 3x = 27$

Divide 3 on both sides to isolate the coefficient from x.

$\implies \dfrac{3x}{3} = \dfrac{27}{3}$

$\implies \boxed{x = 9}$

Check:

Now, let's check our answer. This can be done by substituting the obtained value of "x", into the given equation and simplifying it.

Correct/Incorrect:

If L.H.S = R.H.S, then the value of "x" is correct.

If L.H.S ≠ R.H.S, then we might have to recheck our work we did above.

$\implies -4(2x + 5) + 5x - 1 = -48$

Plugging x = 9 into the equation:

$\implies -4[2(9) + 5] + 5(9) - 1 = -48$

Simplifying the expression using PEMDAS:

$\implies -4[18 + 5] + 5(9) - 1 = -48$

Simplifying the expression inside the parentheses (18 + 5) and evaluating the product of 5 and 9:

$\implies -4[23] + 45 - 1 = -48$

Opening the parentheses "-4[23]" and multiplying -4 and 23

$\implies -92 + 45 - 1 = -48$

Subtracting 45 both sides of the equation:

$\implies -92 - 1 = -48 - 45$

$\implies -92 - 1 = -93$

Simplifying the L.H.S:

$\implies -93 = -93 \ \checkmark \checkmark$

Therefore, our answer is correct.