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Can anyone please help me solve this and show how you did it? Thank you so much!

-3(-2w-6)<=10-2(-2w-4.5)

(WILL GIVE OUT 50 POINTS!!)

Sagot :

ashygurlllllll
Step by Step Solution
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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the less equal sign from both sides of the inequality :

-3*(-2*w-6)-(10-2*(-2*w-(45/10)))≤0

Step by step solution :

STEP
1
:

9
Simplify —
2
Equation at the end of step
1
:

9
(0-(3•(-2w-6)))-(10-(2•(-2w-—))) ≤ 0
2
STEP
2
:
Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 2 as the denominator :

-2w -2w • 2
-2w = ——— = ———————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-2w • 2 - (9) -4w - 9
————————————— = ———————
2 2
Equation at the end of step
2
:

(-4w-9)
(0-(3•(-2w-6)))-(10-(2•———————)) ≤ 0
2
STEP
3
:

STEP
4
:

Pulling out like terms :

4.1 Pull out like factors :

-4w - 9 = -1 • (4w + 9)

Equation at the end of step
4
:

(0 - (3 • (-2w - 6))) - (10 - (-4w - 9)) ≤ 0
STEP
5
:

STEP
6
:

Pulling out like terms :

6.1 Pull out like factors :

-2w - 6 = -2 • (w + 3)

Equation at the end of step
6
:

(0 - -6 • (w + 3)) - (4w + 19) ≤ 0
STEP
7
:

Equation at the end of step
7
:

2w - 1 ≤ 0
STEP
8
:

8.1 Divide both sides by 2

w-(1/2) ≤ 0


Solve Basic Inequality :

8.2 Add 1/2 to both sides

w ≤ 1/2


Inequality Plot :

8.3 Inequality plot for

2.000 w - 1.000 ≤ 0



One solution was found :
w ≤ 1/2
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