Question

How many solutions does the equation 5x + 3x –4 = 10 have?


Zero
One
Two
Infinitely many

Answer 1

if you can't tell me right away, then lets solve this equatin.

Answer 2

Do you see any like terms on the left hand side of the equation ?

Answer 3

no

Answer 4

I will color the like terms in blue
\(\large\color{black}{ \displaystyle \color{blue}{5x} + \color{blue}{3x} -4 = 10 }\)

Answer 5

Add the x 's. What is \(\normalsize\color{black}{ \displaystyle \color{blue}{5x+} \color{blue}{3x} }\) ?

Answer 6

8x

Answer 7

yes, so
\(\large\color{black}{ \displaystyle \color{blue}{5x} + \color{blue}{3x} -4 = 10 }\)
\(\large\color{black}{ \displaystyle \color{blue}{8x} -4 = 10 }\)

Answer 8

now, you have variables (x's ) and numbers (the -4 in this case) on left side
and on right side you have a number.

can you eliminate the variables for me?

Answer 9

lets add 4 to both sides
\(\large\color{black}{ \displaystyle 8x-4 \color{darkgoldenrod}{\bf +4} = 10\color{darkgoldenrod}{\bf +4} }\)

Answer 10

what is -4+4 = ?

Answer 11

0

Answer 12

yes, and 10+4

Answer 13

is?

Answer 14

14

Answer 15

Yup !!
\(\large\color{black}{ \displaystyle 8x-4 \color{darkgoldenrod}{\bf +4} = 10\color{darkgoldenrod}{\bf +4} }\)
\(\large\color{black}{ \displaystyle 8x+0= 14 }\)

so we now have just
\(\large\color{black}{ \displaystyle 8 \times x = 14 }\)

Answer 16

by what do you divide on both sides, to solve for x (to isolate the x) ?

Answer 17

?

Answer 18

so is there only one posibiltity to make an equation?

Answer 19

or is there more?

Answer 20

\(\large\color{black}{ \displaystyle 8x= 14 }\)
alright, I will tell you.
We have to divide by 8 on both sides

\(\large\color{black}{ \displaystyle 8x \color{magenta}{\div 8}= 14 \color{magenta}{\div 8} }\)

Answer 21

yes, correct there is only one solution

Answer 22

\(\large\color{black}{ \displaystyle 8x \color{magenta}{\div 8}= 14 \color{magenta}{\div 8} }\)
\(\large\color{black}{ \displaystyle \cancel{8}x \color{magenta}{\div \cancel{8}}= 14 \color{magenta}{\div 8} }\)
\(\large\color{black}{ \displaystyle x= 14 \color{magenta}{\div 8} }\)

Answer 23

x=14/8
x=7/4

Answer 24

and it is x=7/4

Answer 25

ok thanks for the help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!SolomonZelman

Answer 26

sure