1-13x≥12⋅(x-35)

Combine x and 13.

1-x3≥12⋅(x-35)

Apply the distributive property.

1-x3≥12x+12(-35)

Combine 12 and x.

1-x3≥x2+12(-35)

Multiply 12(-35).

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

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.

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.

Simplify the numerator.

Factor x out of -x⋅2-x⋅3.

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

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.

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. 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.

Multiply -1 by -1.

15×6≤-1310⋅-1

Multiply 5×6 by 1.

5×6≤-1310⋅-1

5×6≤-1310⋅-1

Multiply -1310⋅-1.

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)

Cancel the common factor of 2.

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 in 5x≤395 by 5.

5×5≤395⋅15

Cancel the common factor of 5.

Cancel the common factor.

5×5≤395⋅15

Divide x by 1.

x≤395⋅15

x≤395⋅15

Multiply 395⋅15.

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)