Answer: q ≤ -163/10
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "4.3" was replaced by "(43/10)". 3 more similar replacement(s)
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater equal sign from both sides of the inequality :
-(53/10)-((67/10)+(43/10)+q)≥0
Step by step solution :
Step 1 :
43
Simplify ——
10
Equation at the end of step 1 :
53 67 43
(0-——)-((——+——)+q) ≥ 0
10 10 10
Step 2 :
67
Simplify ——
10
Equation at the end of step 2 :
53 67 43
(0 - ——) - ((—— + ——) + q) ≥ 0
10 10 10
Step 3 :
Adding fractions which have a common denominator :
3.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
67 + 43 11
——————— = ——
10 1
Equation at the end of step 3 :
53 11
(0 - ——) - (—— + q) ≥ 0
10 1
Step 4 :
53
Simplify ——
10
Equation at the end of step 4 :
53
(0 - ——) - (q + 11) ≥ 0
10
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 10 as the denominator :
q + 11 (q + 11) • 10
q + 11 = —————— = —————————————
1 10
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 :
5.2 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:
-53 - ((q+11) • 10) -10q - 163
——————————————————— = ——————————
10 10
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
-10q - 163 = -1 • (10q + 163)
Equation at the end of step 6 :
-10q - 163
—————————— ≥ 0
10
Step 7 :
7.1 Multiply both sides by 10
7.2 Multiply both sides by (-1)
Flip the inequality sign since you are multiplying by a negative number
10q+163 ≤ 0
7.3 Divide both sides by 10
q+(163/10) ≤ 0
