Solve for x 1-1/3x>=1/2*(x-3/5)

Math
1-13x≥12⋅(x-35)
Combine x and 13.
1-x3≥12⋅(x-35)
Simplify 12⋅(x-35).
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Apply the distributive property.
1-x3≥12x+12(-35)
Combine 12 and x.
1-x3≥x2+12(-35)
Multiply 12(-35).
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Multiply 12 and 35.
1-x3≥x2-32⋅5
Multiply 2 by 5.
1-x3≥x2-310
1-x3≥x2-310
1-x3≥x2-310
Move all terms containing x to the left side of the inequality.
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Subtract x2 from both sides of the inequality.
1-x3-x2≥-310
To write -x3 as a fraction with a common denominator, multiply by 22.
1-x3⋅22-x2≥-310
To write -x2 as a fraction with a common denominator, multiply by 33.
1-x3⋅22-x2⋅33≥-310
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
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Multiply x3 and 22.
1-x⋅23⋅2-x2⋅33≥-310
Multiply 3 by 2.
1-x⋅26-x2⋅33≥-310
Multiply x2 and 33.
1-x⋅26-x⋅32⋅3≥-310
Multiply 2 by 3.
1-x⋅26-x⋅36≥-310
1-x⋅26-x⋅36≥-310
Combine the numerators over the common denominator.
1+-x⋅2-x⋅36≥-310
Simplify each term.
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Simplify the numerator.
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Factor x out of -x⋅2-x⋅3.
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Factor x out of -x⋅2.
1+x(-1⋅2)-x⋅36≥-310
Factor x out of -x⋅3.
1+x(-1⋅2)+x(-1⋅3)6≥-310
Factor x out of x(-1⋅2)+x(-1⋅3).
1+x(-1⋅2-1⋅3)6≥-310
1+x(-1⋅2-1⋅3)6≥-310
Multiply -1 by 2.
1+x(-2-1⋅3)6≥-310
Multiply -1 by 3.
1+x(-2-3)6≥-310
Subtract 3 from -2.
1+x⋅-56≥-310
1+x⋅-56≥-310
Move -5 to the left of x.
1+-5⋅x6≥-310
Move the negative in front of the fraction.
1-5×6≥-310
1-5×6≥-310
1-5×6≥-310
Move all terms not containing x to the right side of the inequality.
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Subtract 1 from both sides of the inequality.
-5×6≥-310-1
To write -1 as a fraction with a common denominator, multiply by 1010.
-5×6≥-310-1⋅1010
Combine -1 and 1010.
-5×6≥-310+-1⋅1010
Combine the numerators over the common denominator.
-5×6≥-3-1⋅1010
Simplify the numerator.
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Multiply -1 by 10.
-5×6≥-3-1010
Subtract 10 from -3.
-5×6≥-1310
-5×6≥-1310
Move the negative in front of the fraction.
-5×6≥-1310
-5×6≥-1310
Multiply each term in -5×6≥-1310 by -1
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Multiply each term in -5×6≥-1310 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-5×6⋅-1≤-1310⋅-1
Multiply -5×6⋅-1.
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Multiply -1 by -1.
15×6≤-1310⋅-1
Multiply 5×6 by 1.
5×6≤-1310⋅-1
5×6≤-1310⋅-1
Multiply -1310⋅-1.
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Multiply -1 by -1.
5×6≤1(1310)
Multiply 1310 by 1.
5×6≤1310
5×6≤1310
5×6≤1310
Multiply both sides of the equation by 6.
5x≤1310⋅(6)
Simplify 1310⋅(6).
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Cancel the common factor of 2.
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Factor 2 out of 10.
5x≤132(5)⋅6
Factor 2 out of 6.
5x≤132⋅5⋅(2⋅3)
Cancel the common factor.
5x≤132⋅5⋅(2⋅3)
Rewrite the expression.
5x≤135⋅3
5x≤135⋅3
Combine 135 and 3.
5x≤13⋅35
Multiply 13 by 3.
5x≤395
5x≤395
Divide each term by 5 and simplify.
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Divide each term in 5x≤395 by 5.
5×5≤395⋅15
Cancel the common factor of 5.
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Cancel the common factor.
5×5≤395⋅15
Divide x by 1.
x≤395⋅15
x≤395⋅15
Multiply 395⋅15.
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Multiply 395 and 15.
x≤395⋅5
Multiply 5 by 5.
x≤3925
x≤3925
x≤3925
The result can be shown in multiple forms.
Inequality Form:
x≤3925
Interval Notation:
(-∞,3925]
Solve for x 1-1/3x>=1/2*(x-3/5)

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