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

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thomasarianna8082 thomasarianna8082

23-05-2022
Mathematics

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

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Аноним Аноним · Answer 1 · 2022-05-23T23:17:46+02:00

[tex]\tt x=9[/tex]

Step-by-step explanation:

[tex]\tt -4(2x + 5) + 5x - 1 = - 48[/tex]

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

[tex]\tt -8x-20+5x-1=-48[/tex]

Combine like terms:-

[tex]\tt -3x-21=-48[/tex]

Add 21 to both sides:-

[tex]\tt -3x=-48+21[/tex]

[tex]\tt -3x=-27[/tex]

Divide both sides by -3:-

[tex]\tt \: x = \cfrac{ - 27}{ - 3} [/tex]

[tex]\tt x=9[/tex]

Hope this answers your question!

IBrainlyExpertI IBrainlyExpertI · Answer 2 · 2022-05-24T01:20:30+02:00

Answer:

x = 9

Step-by-step explanation:

Given equation:

[tex]-4(2x + 5) + 5x - 1 = -48[/tex]

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

[tex]\implies -4(2x + 5) + 5x - 1 = -48[/tex]

[tex]\implies (2x \times -4) + (4 \times 5) + 5x - 1 = -48[/tex]

[tex]\implies -8x - 20 + 5x - 1 = -48[/tex]

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

[tex]\implies -8x - 20 + 5x - 1 = -48[/tex]

[tex]\implies x(-8 + 5) + 1(-20 - 1) = -48[/tex]

[tex]\implies x(-3) - 21 = -48[/tex]

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

[tex]\implies-3x + 21 - 21 = -48 + 21[/tex]

[tex]\implies -3x = -27[/tex]

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

[tex]\implies 3x = 27[/tex]

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

[tex]\implies \dfrac{3x}{3} = \dfrac{27}{3}[/tex]

[tex]\implies \boxed{x = 9}[/tex]

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.

[tex]\implies -4(2x + 5) + 5x - 1 = -48[/tex]

Plugging x = 9 into the equation:

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

Simplifying the expression using PEMDAS:

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

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

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

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

[tex]\implies -92 + 45 - 1 = -48[/tex]

Subtracting 45 both sides of the equation:

[tex]\implies -92 - 1 = -48 - 45[/tex]

[tex]\implies -92 - 1 = -93[/tex]

Simplifying the L.H.S:

[tex]\implies -93 = -93 \ \checkmark \checkmark[/tex]

Therefore, our answer is correct.