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
