# Solve for x 1/3x+2/5x-1/2*(x+3)<=1/10

13x+25x-12⋅(x+3)≤110
Factor the inequality.
Combine 13 and x.
x3+25x-12⋅(x+3)≤110
Combine 25 and x.
x3+2×5-12⋅(x+3)≤110
Apply the distributive property.
x3+2×5-12x-12⋅3≤110
Combine x and 12.
x3+2×5-x2-12⋅3≤110
Multiply -12⋅3.
Multiply 3 by -1.
x3+2×5-x2-3(12)≤110
Combine -3 and 12.
x3+2×5-x2+-32≤110
x3+2×5-x2+-32≤110
Move the negative in front of the fraction.
x3+2×5-x2-32≤110
To write x3 as a fraction with a common denominator, multiply by 55.
x3⋅55+2×5-x2-32≤110
To write 2×5 as a fraction with a common denominator, multiply by 33.
x3⋅55+2×5⋅33-x2-32≤110
Write each expression with a common denominator of 15, by multiplying each by an appropriate factor of 1.
Multiply x3 and 55.
x⋅53⋅5+2×5⋅33-x2-32≤110
Multiply 3 by 5.
x⋅515+2×5⋅33-x2-32≤110
Multiply 2×5 and 33.
x⋅515+2x⋅35⋅3-x2-32≤110
Multiply 5 by 3.
x⋅515+2x⋅315-x2-32≤110
x⋅515+2x⋅315-x2-32≤110
Combine the numerators over the common denominator.
x⋅5+2x⋅315-x2-32≤110
To write x⋅5+2x⋅315 as a fraction with a common denominator, multiply by 22.
x⋅5+2x⋅315⋅22-x2-32≤110
To write -x2 as a fraction with a common denominator, multiply by 1515.
x⋅5+2x⋅315⋅22-x2⋅1515-32≤110
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply x⋅5+2x⋅315 and 22.
(x⋅5+2x⋅3)⋅215⋅2-x2⋅1515-32≤110
Multiply 15 by 2.
(x⋅5+2x⋅3)⋅230-x2⋅1515-32≤110
Multiply x2 and 1515.
(x⋅5+2x⋅3)⋅230-x⋅152⋅15-32≤110
Multiply 2 by 15.
(x⋅5+2x⋅3)⋅230-x⋅1530-32≤110
(x⋅5+2x⋅3)⋅230-x⋅1530-32≤110
Combine the numerators over the common denominator.
(x⋅5+2x⋅3)⋅2-x⋅1530-32≤110
Reorder terms.
-1⋅(15x)+2(x⋅5+2x⋅3)30-32≤110
Combine -1⋅15x+2(x⋅5+2x⋅3)30 and -32 using a common denominator.
Move x.
-1⋅(15x)+2(5⋅x+2⋅(3x))30-32≤110
To write -32 as a fraction with a common denominator, multiply by 1515.
-1⋅(15x)+2(5⋅x+2⋅(3x))30-32⋅1515≤110
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply 32 and 1515.
-1⋅(15x)+2(5⋅x+2⋅(3x))30-3⋅152⋅15≤110
Multiply 2 by 15.
-1⋅(15x)+2(5⋅x+2⋅(3x))30-3⋅1530≤110
-1⋅(15x)+2(5⋅x+2⋅(3x))30-3⋅1530≤110
Combine the numerators over the common denominator.
-1⋅(15x)+2(5⋅x+2⋅(3x))-3⋅1530≤110
-1⋅(15x)+2(5⋅x+2⋅(3x))-3⋅1530≤110
Rewrite -1⋅15x+2(5⋅x+2⋅3x)-3⋅1530 in a factored form.
Multiply -1 by 15.
-15x+2(5x+2⋅(3x))-3⋅1530≤110
Multiply 2 by 3.
-15x+2(5x+6x)-3⋅1530≤110
-15x+2(11x)-3⋅1530≤110
Multiply 11 by 2.
-15x+22x-3⋅1530≤110
Multiply -3 by 15.
-15x+22x-4530≤110
7x-4530≤110
7x-4530≤110
7x-4530≤110
Solve the inequality.
Multiply both sides of the equation by 30.
7x-45≤110⋅(30)
Remove parentheses.
7x-45≤110⋅(30)
Cancel the common factor of 10.
Factor 10 out of 30.
7x-45≤110⋅(10(3))
Cancel the common factor.
7x-45≤110⋅(10⋅3)
Rewrite the expression.
7x-45≤3
7x-45≤3
Move all terms not containing x to the right side of the inequality.
Add 45 to both sides of the inequality.
7x≤3+45
7x≤48
7x≤48
Divide each term by 7 and simplify.
Divide each term in 7x≤48 by 7.
7×7≤487
Cancel the common factor of 7.
Cancel the common factor.
7×7≤487
Divide x by 1.
x≤487
x≤487
x≤487
x≤487
The result can be shown in multiple forms.
Inequality Form:
x≤487
Interval Notation:
(-∞,487]
Solve for x 1/3x+2/5x-1/2*(x+3)<=1/10