What is the solution set for the inequality -2(3x - 4) + 5 \leq -x + 3? — SAT

What is the solution set for the inequality $-2(3x - 4) + 5 \leq -x + 3$ ?

A
$x \leq 2$
B
$x \geq -\frac{6}{5}$
$x \geq 2$ Cevap
D
$x \geq \frac{10}{7}$

Cevap

x \geq 2

Distributing

-2

over

3x - 4

yields

-6x + 8

. Combining the constants on the left gives

-6x + 13 \leq -x + 3

. Subtracting

13

and adding

x

to both sides results in

-5x \leq -10

. Dividing both sides by

-5

and flipping the inequality symbol yields the solution set of all values greater than or equal to

2

Adım Adım Çözüm

Distribute the

-2

coefficient on the left side of the inequality.

-6x + 8 + 5 \leq -x + 3

Applying the distributive property simplifies the expression inside the parentheses.

Combine the constant terms on the left side of the inequality.

-6x + 13 \leq -x + 3

Combining like terms simplifies the left-hand side before isolating the variable.

Subtract

13

from both sides of the inequality.

-6x \leq -x - 10

This begins the process of isolating the variable terms on one side and constant terms on the other.

Add

x

to both sides of the inequality.

-5x \leq -10

This groups all variable terms together on the left-hand side.

Divide both sides of the inequality by

-5

and reverse the direction of the inequality sign.

x \geq 2

Dividing an inequality by a negative number requires reversing the inequality sign to maintain a true statement.

Anahtar Kavram

Solving linear inequalities in one variable using algebraic properties, specifically distributing a negative value and reversing the inequality direction when dividing by a negative number.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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