Question

name
extended practice: multi - step equations (intermediate
directions: solve each equation for x.
(01) (5x - 4=2x + 11)
(02) (-2(x + 9)=4x + 12)
(03) (3(x - 6)+8 = 2x + 5)
(04) (4+\frac{2x}{3}=6)
(05) (4x - 7=2(2x - 5))
(06) (2x + 9=5x + 21)
(07) (-3(x - 8)+6=-12)
(08) (10x - 4=6x + 20)
(09) (7=\frac{5x}{2}-3)
(10) (6(x - 4)+2 = 2x + 10)
(11) (4(x - 5)+3x=3(x - 2)+15)
(12) (9x - 2(3x - 4)=8)
(13) (-4(x + 6)+8 = 12x - 20)
(14) (-3+\frac{3x}{4}=0)
(15) (-7(x - 3)=2x - 35)
(16) (-5(x - 6)-2x = 8x + 2)
(17) (-3x + 5=2x - 10)
(18) (6(x + 3)-4 = 5x + 8)
(19) (-2(x - 9)+7 = 3x - 15)
(20) (8x - 6=4(x + 3)-2)
(21) (-5x + 10=-2x + 40)
(22) (-4(x + 7)=12 - 2x)
(23) (\frac{6x}{5}+4 = 10)
(24) (2(x - 8)-3=-4x + 17)

Explanation:

Let's solve one of these equations, say problem (01): \( 5x - 4 = 2x + 11 \)

Step 1: Subtract \( 2x \) from both sides

To get the \( x \)-terms on one side, we subtract \( 2x \) from both sides.
\( 5x - 2x - 4 = 2x - 2x + 11 \)
\( 3x - 4 = 11 \)

Step 2: Add 4 to both sides

To isolate the term with \( x \), we add 4 to both sides.
\( 3x - 4 + 4 = 11 + 4 \)
\( 3x = 15 \)

Step 3: Divide by 3

To solve for \( x \), we divide both sides by 3.
\( \frac{3x}{3} = \frac{15}{3} \)
\( x = 5 \)

Answer:

\( x = 5 \)

If you want solutions to other equations, please specify which one, and I'll be happy to solve it!