How do you solve #3|2x + -5| + 3 = 42#?

Question

Eli Assouline · Accepted Answer

#x=9 or x=-4#

Here, #3|2x+(-5)|+3=42,#

Adding #(-3)# both sides

#3|2x+(-5)|+3+(-3)=42+(-3)#

#=>3|2x+(-5)|=39,#

Dividing both sides by 3

#(cancel(3)|2x+(-5)|)/(cancel(3))=39/3=>|2x+(-5)|=13#

#2x+(-5)=13or2x+(-5)=-13#

Adding #5# both sides

#2x+(-5)+5=13+5or2x+(-5)+5=-13+5#

#=>2x=18 or 2x=-8=>x=9 or x=-4#

Genesis Allen · Answer

#x=-4,9#

Solve:

#3abs(2x+ -5)+3=42#

Make the absolute value simpler.

#3abs(2x-5)+3=42#

Subtract #3# from both sides of the equation.

#3abs(2x-5)+3-3=42-3#

Simplify.

#3abs(2x-5)+0=39#

#3abs(2x-5)=39#

Divide both sides by #3#.

#(cancel(3)^1abs(2x-5))/cancel(3)^1=cancel39^13/cancel(3)^1#

Simplify.

#abs(2x-5)=13#

Since #abs(+-a)=a#, we can break the equation into two equations:

#2x-5=13# and #-(2x-5)=13#

ด ฟฟ ฟฟ

First, solve the following equation:

Add #5# to both sides of the equation.

#2x-5+5=13+5#

Simplify.

#2x=18#

Divide both sides by #2#.

#(cancel(2)^1x)/cancel(2)^1=cancel18^9/cancel2^1#

Simplify.

#x=9#

ด ฟฟ ฟฟ

Complete the second equation:

#-(2x-5)=13#

Expand.

#-2x+5=13#

Subtract #5# from both sides.

#-2x+5-5=13-5#

Simplify.

#-2x+0=8#

#-2x=8#

Divide both sides by #-2#.

#(cancel(-2)^1x)/(cancel(-2)^1)=cancel8^4/(cancel(-2)^1#

Simplify.

#x=-4#

ด ฟฟ ฟฟ

#x=-4,9#

Abigail Allen · Answer

undefined To solve the equation $3|2x - 5| + 3 = 42$, follow these steps:

1. Subtract 3 from both sides of the equation to isolate the absolute value term.

$$3|2x - 5| = 39$$

2. Divide both sides of the equation by 3 to isolate the absolute value term.

$$|2x - 5| = \frac{39}{3}$$

$$|2x - 5| = 13$$

3. Now, you have two cases to consider for the absolute value:

a) $2x - 5 = 13$

b) $2x - 5 = -13$

4. Solve each case separately:

a) For $2x - 5 = 13$:

$$2x = 13 + 5$$
$$2x = 18$$
$$x = \frac{18}{2}$$
$$x = 9$$

b) For $2x - 5 = -13$:

$$2x = -13 + 5$$
$$2x = -8$$
$$x = \frac{-8}{2}$$
$$x = -4$$

5. Therefore, the solutions to the equation $3|2x - 5| + 3 = 42$ are $x = 9$ and $x = -4$.

Savannah Anderson · Answer

undefined To solve the equation $3|2x - 5| + 3 = 42$, follow these steps:

1. Subtract 3 from both sides to isolate the absolute value term.
2. Divide both sides by 3.
3. Solve for $|2x - 5|$ by isolating it on one side of the equation.
4. Once you have $|2x - 5|$ isolated, set up two equations: one positive and one negative, equating the expression within the absolute value bars to both positive and negative values.
5. Solve each equation separately.
6. Check the solutions obtained by plugging them back into the original equation to ensure they are valid.

The solutions will depend on the specific values of $x$ that satisfy the conditions of the equations formed in step 4.