How do you solve #4(x – 3) + 4

Question

How do you solve #4(x – 3) + 4 <10 + 6x#?

Abigail Allen · Accepted Answer

#x>9#

Expand the bracket on the LHS by multiplying #x# with #4# and #-3# with #4#.

#4x-12+4<10+6x#

#4x-8<10+6x#

#4x<18+6x#

#-2x<18#

Now, divide the entire equation by #-2#. But keep in mind the the equality sign FLIPS when you divide by a negative number.

#x>9#

Below is the graph of this inequalities.

graph{x>9 [-0.76, 72.3, 0.74, 37.27]}

Eli Assouline · Answer

See a solution process below:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis: #color(red)(4)(x - 3) + 4 < 10 + 6x# #(color(red)(4) * x) - (color(red)(4) * 3) + 4 < 10 + 6x# #4x - 12 + 4 < 10 + 6x# #4x - 8 < 10 + 6x# Next, subtract #color(red)(4x)# and #color(blue)(10)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced: #4x - 8 - color(red)(4x) - color(blue)(10) < 10 + 6x - color(red)(4x) - color(blue)(10)# #4x - color(red)(4x) - 8 - color(blue)(10) < 10 - color(blue)(10) + 6x - color(red)(4x)# #0 - 18 < 0 + (6 - color(red)(4))x# #-18 < 2x# Now, divide each side of the inequality by #color(red)(2)# to solve for #x# while keeping the equation balanced: #-18/color(red)(2) < (2x)/color(red)(2)# #-9 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))# #-9 < x# To state the solution in terms of #x# we can reverse or "flip" the entire inequality: #x > -9#

Eli Assouline · Answer

undefined To solve the inequality 4(x - 3) + 4 < 10 + 6x, you would first distribute 4 to the terms inside the parentheses. Then, you would combine like terms on both sides of the inequality. After that, isolate the variable term by subtracting 4x from both sides and then dividing both sides by 2. The solution is x > 2.

How do you solve #4(x – 3) + 4 &lt;10 + 6x#?

How do you solve #4(x – 3) + 4 <10 + 6x#?