What is (3x-1)(x+5)-1<= 3(x-2)+21x ?

The solution to (3x-1)(x+5)-1<= 3(x-2)+21x is 0<= x<= 10/3

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(3x-1)(x+5)-1<= 3(x-2)+21x

(3 x - 1) (x + 5) - 1 \leq 3 (x - 2) + 21 x

0 \leq x \leq \frac{10}{3}

Interval Notation

[0, \frac{10}{3}]

Decimal

0 \leq x \leq 3.33333 \dots

Solution steps

(3 x - 1) (x + 5) - 1 \leq 3 (x - 2) + 21 x

Rewrite in standard form

3 x^{2} - 10 x \leq 0

Factor

3 x^{2} - 10 x : x (3 x - 10)

x (3 x - 10) \leq 0

Identify the intervals

0 \leq x \leq \frac{10}{3}

\frac{4}{( 3 x - 2 )} \leq - 2

3 x^{2} - 8 < - 2 x

\frac{( x - 1 ) ( x - 2 ) ^{3} ( x - 4 ) ^{2}}{x + 3} \geq 0

x^{3} + 5 x^{2} + 4 x > 0

m^{2} > 3

What is (3x-1)(x+5)-1<= 3(x-2)+21x ?
The solution to (3x-1)(x+5)-1<= 3(x-2)+21x is 0<= x<= 10/3