Math

QuestionIs the equation 4x1+8x=74x - 1 + 8x = 7 true? Yes or No.

Studdy Solution

STEP 1

Assumptions1. We are given a series of mathematical expressions and we need to verify if they hold true. . The operations involved are multiplication, addition, and subtraction.

STEP 2

Let's start by simplifying the first expression.
4x1+8x=74x -1 +8x =7

STEP 3

Combine like terms.
12x1=712x -1 =7

STEP 4

Next, we have the expression1+823=7-1 +8 \cdot \frac{2}{3} =7

STEP 5

Perform the multiplication.
1+163=7-1 + \frac{16}{3} =7

STEP 6

Convert -1 to a fraction with denominator3 to add it with 163\frac{16}{3}.
33+163=\frac{-3}{3} + \frac{16}{3} =

STEP 7

Perform the addition.
133=7\frac{13}{3} =7

STEP 8

Convert the fraction to a decimal.
4.3374.33 \approx7

STEP 9

Next, we have the expression83+823=7\frac{8}{3} - +8 \cdot \frac{2}{3} =7

STEP 10

Perform the multiplication.
83+163=7\frac{8}{3} - + \frac{16}{3} =7

STEP 11

Convert - to a fraction with denominator3 to add it with the other fractions.
8333+163=7\frac{8}{3} - \frac{3}{3} + \frac{16}{3} =7

STEP 12

Perform the addition and subtraction.
21=7\frac{21}{} =7

STEP 13

Convert the fraction to a decimal.
7=77 =7

STEP 14

Now, we have the expression=7=7

STEP 15

This is just a number, so it doesn't need any simplification.

STEP 16

Now, let's compare the results of each expression with the number.
The first expression, 12x=12x - =, is not equivalent to without knowing the value of xx.
The second expression, 4.334.33 \approx, is not equivalent to.
The third expression, = =, is equivalent to.
The fourth expression, ==, is equivalent to.
So, the given series of expressions does not hold true for all cases.
Therefore, the answer is No.

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