How do you solve #8(x+3) = 5x-(14-2x)+48#?

Question

Julia Adams · Accepted Answer

#color(maroon(x = 10# #8(x + 3) = 5x - (14 - 2x) + 48# #8x + 24 = 5x - 14 + 2x + 48, " removing braces"# #8x - 5x - 2x = -14 + 48 - 24, " bringing like terms together"# #color(maroon(x = 10#

Julia Adams · Answer

#x = 10#

#8(x+3) = 5x - (14-2x) = 48#

First, use the distributive property (shown below) to simplify #8(x+3)# and #-(14-2x)#

Following this image, we know that:
#color(blue)(8(x+3) = (8 * x) + (8 * 3) = 8x + 24)#
and
#color(blue)(-(14-2x) = -14 + 2x)#

Put them back into the equation:
#8x + 24 = 5x - 14 + 2x + 48#

Combine like terms on the right hand side:
#8x + 24 = 7x + 34#

Subtract #color(blue)(7x)# from both sides:
#8x + 24 quadcolor(blue)(-quad7x) = 7x + 34 quadcolor(blue)(-quad7x)#

#x + 24 = 34#

Subtract #color(blue)24# from both sides:
#x + 24 quadcolor(blue)(-quad24) = 34 quadcolor(blue)(-quad24)#

Therefore,
#x = 10#

Hope this helps!

Eli Assouline · Answer

undefined To solve the equation 8(x+3) = 5x-(14-2x)+48:

1. Distribute the 8 on the left side and simplify the expression: 8x + 24 = 5x - 14 + 2x + 48.
2. Combine like terms: 8x + 24 = 7x + 34.
3. Subtract 7x from both sides: 8x - 7x + 24 = 7x - 7x + 34.
4. Simplify: x + 24 = 34.
5. Subtract 24 from both sides: x + 24 - 24 = 34 - 24.
6. Simplify: x = 10.