A) The simplified Expression 0.8(2x + x) + 3(7 - 4.1x) =
is -
![(21)/(22.8)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/rkl2rao83ngkrtb2gvwaoau49rjghttest.png)
B) The value of y is
![(3x)/(5)\].](https://img.qammunity.org/2024/formulas/mathematics/high-school/5vo944mzf73uox9v35e5dlrg18kcd9lf6u.png)
C) The value of x is 3/2
D) The simplified expression is 1343x + 981y = 0
A) Simplifying the Expression:
![\[0.8(2x + x) + 3(7 - 4.1x) = (x + 21)/(2)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/vjdslt09zays0q0pnm9vqztke4shfwapvt.png)
The first step is to distribute the coefficients and combine like terms:
![\[1.6x + 0.8x + 21 - 12.3x = (x + 21)/(2)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/5oo7si6k7y7sxmm172zudy2v23qv0i1ct0.png)
Combining like terms on the left side gives:
![\[-10.9x + 21 = (x + 21)/(2)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/clinkdmdpblze8si14oq2qaj6vysm7m9q3.png)
Multiply both sides by 2 to eliminate the fraction:
-21.8x + 42 = x + 21
Now, solve for \(x\):
![\[x = (21 - 42)/(1 + 21.8) = -(21)/(22.8)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/f6sozpvqw74xho3805d254jj8e17pcm56g.png)
B) Solving for y:
![\[12 = (6x + 22y)/(x + y)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/rn88wci3onj94ab8jdgjxh2nfzwilvvvyu.png)
Multiply both sides by \(x + y\) to eliminate the fraction:
![\[12(x + y) = 6x + 22y\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/ls5k9u5nzuqvj2dmhdldh64x1uvvcl8yty.png)
Distribute and simplify:
![\[12x + 12y = 6x + 22y\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/8sv6evsha40g0wsqysp146kke9xqu2syye.png)
Isolate \(y\) on one side:
12y - 22y = 6x - 12x
Combine like terms:
-10y = -6x
Solve for \(y\):
![\[y = (3x)/(5)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/czc4m6uicazm8cphvolkyztjj9ndukcupo.png)
C) Solving for x:
(3x - (6x + 1) = -3x - 2
Expand the parentheses and simplify:
3x - 6x - 1 = -3x - 2
Combine like terms and isolate \(x\):
-3x = -2
Solve for \(x\):
x = 3/2
**D) Simplifying the Expression:**
![\[112 = (x + 27y)/(12x + 9y)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/tw3z6008tgymp4cxnugmixozuhlalk14lk.png)
Multiply both sides by the denominator to eliminate the fraction:
![\[112(12x + 9y) = x + 27y\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/hdny2shckkzbf30f35i1er78y86zfdf66p.png)
Distribute and simplify:
1344x + 1008y = x + 27y
Combine like terms:
1343x + 981y = 0
This is the simplified expression.
The probable question may be:
A) Simplify the Expression:
\[0.8(2x + x) + 3(7 - 4.1x) = \frac{x + 21}{2}\]
B) Solve for y:
\[12 = \frac{6x + 22y}{x + y}\]
C) Solve for x:
\[(3x - \_\_\_) - (6x + 1) = -3x - 2\]
D) Simplify the Expression:
\[112 = \frac{x + 27y}{12x + 9y}\]