Math Problem Statement
Solve for x in the given equations and match the answers to determine the 4-letter code.
Solution
Let's solveLet's each solve equation each step equation by step step by and step match and the find solutions the to corresponding the answers **:
answer---
choices###** to1 determine. the Solve ** for4 (-letter x code **):.
###[
10 -1 5x = 14 -. x
]
** SolveStep 1: for Combine x like: terms. (
Move ( - x10 \ -) to5 thex left =:
14\ -[
x- \5)x**
+1 x. = Combine like14 terms -:
10
[
]
Simplify:
−4x=4
10** -Step 25x:** = Solve for ( x14 \ -): x
\ ]
x = Sub \tractfrac \({ 410}{ \-)4 from} both = sides -:
1
\\[
]
-**5x = 4Answer:** - x
2. Add x \ \() x to = -1 → Code letter F.
both### sides2.:
Solve for x \:[
\ -[
5x +- x = 44
x - \ ]
8 = Simpl -(ify5:
x + \ [
3 )
-\4]x
=** Step4
1 :** \ Dis]
tribute3 the. negative Divide sign by on ( the - right4: \
):
\ [
-[
4 xx = -1 -
8 \ =]
-**5Answerx - choice: 3 (
G \)]
(xStep 2: Move =−−5x to the left1:
---
= -3 +### 8
**\2]
Simplify.: Solve
for\ x[
x = : \( -5$$
**Answer:** $$x4 = 5$$ → Codex - letter **H**.
---
###8 = -( 53. Solve for $$x$$:
x$$+3 x \cdot 34 =) \)**
71. Disxtribute - the ( negativex sign \ oncd theot right 17)$$
** sideStep :
1 :** Simpl $$-ify each term:
\[
12x =4 7x - 17x$$
Combine like terms:
$$12x = -10x$$
**Step 2:** Solve for $$x$$:
$$x - 8 = -12x +5x -10 x3 =
0 \$$
quad2 \.Right Addarrow \( \ quad5 x22 \x) = to both0 sides
:
\ ] \
[
\ [
-x4 =x +0
5\x] =
-**3Answer +:** \(8 x
= \0]
\ ) Simpl →ify Code:
letter ** \G[
** .
x---
=### 54
. Solve \ for]
\(** xAnswer \ choice)::
\(\ H[
\x) - ( x2 = = \5frac)**{
4---
(x### + ** 31.)} Solve{2}
\]
**Step 1:** Simplify the fraction on the right for x: \(: 3x \
\cd[
x - 2 = ot2 (x + 14)
\] =
** 7Step x2:** Distribute \( 2 \ -): (
x\ +[
x17 -) \2 = )2**
x1 + 2
.\]
Simpl**Step ify3:** Move \( the 2x \ left) side to the:
\ left[
12x = 7x - (x + 17)
\]
2:
$$x - 2x = 2 + 2$$
Simplify:
. Dis$$-x = tribute4$$ the
** negativeStep sign :
4:** \ Solve[
for \(12x x = \7x - x): -
17
\ \]
[
x = -4
\]
**Answer:** $$Combine x = -4$$ → Code like letter terms:
$$** A**.
12---
### Final Code:
From the answers:
1 → F,x 2 → H, 3 → G, 4 = → A
**The 4-letter code is:** **FHGA**
---
Would you like further clarification on any of the6 steps? Letx - me know17!
###
Related Questions:$$
31. Sub.tract \( How do 6 you solvex \ linear) equations with from variables both on sides both:
sides? \[
2.6x = - What is the17 distributive property,
and how \ is]
it4 used. Divide in by algebra \(?
63 \.):
How can \ you[
solve equations x involving = fractions - or\ parenthesesfrac?{
174. Why}{6 is combining}
like \ terms]
essentialThis doesn't in match solving any of the choices equations?
5.. **Double-check for rounding How errors do or you check clar if your solution to an equation is correct?
**Tip:** Always simplify both sides of anifications. equation before isolating the variable to make Call asks solving for easier! features plan