What is the complete set of solutions to the inequality -\frac{2}{3}(6x - 9) + 4 > 12? — SAT

What is the complete set of solutions to the inequality $-\frac{2}{3}(6x - 9) + 4 > 12$ ?

A
$x > -\frac{1}{2}$
$x < -\frac{1}{2}$ Cevap
C
$x < -\frac{7}{2}$
D
$x < -2$

Cevap

The inequality is satisfied for all values of

x

such that

x < -\frac{1}{2}

Distributing

-\frac{2}{3}

across

(6x - 9)

yields

-4x + 6

. Adding 4 gives

-4x + 10 > 12

. Subtracting 10 from both sides results in

-4x > 2

. Dividing by

-4

and reversing the inequality sign yields

x < -\frac{1}{2}

Adım Adım Çözüm

Distribute

-\frac{2}{3}

to both terms inside the parentheses:

(6x - 9)

-4x + 6 + 4 > 12

, which simplifies to

-4x + 10 > 12

Applying the distributive property removes the parentheses.

Subtract 10 from both sides of the inequality to isolate the term with

x

-4x > 2

Subtracting 10 from both sides maintains the inequality while simplifying the constant terms.

Divide both sides by

-4

and reverse the inequality sign.

x < -\frac{1}{2}

Dividing both sides of an inequality by a negative number requires reversing the direction of the inequality symbol.

Anahtar Kavram

Solving linear inequalities in one variable requires distributing coefficient terms, combining constants, and reversing the inequality sign when multiplying or dividing by a negative number.

Tahmini Süre:1m 15s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru