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2 years ago

0.2x + 1 = 1.6x + 3.1 What value of x satisfies the equation above?

Mathematics

2 answers:

guapka [62]2 years ago

5 0

Answer:

x = -1.5

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS
Equality Properties

Step-by-step explanation:

Step 1: Define equation

0.2x + 1 = 1.6x + 3.1

Step 2: Solve for x

Subtract 0.2x on both sides: 1 = 1.4x + 3.1
Subtract 3.1 on both sides: -2.1 = 1.4x
Divide both sides by 1.4: -1.5 = x
Rewrite: x = -1.5

Step 3: Check

Plug in x to verify it's a solution.

Substitution: 0.2(-1.5) + 1 = 1.6(-1.5) + 3.1
Multiply: -0.3 + 1 = -2.4 + 3.1
Add: 0.7 = 0.7

bagirrra123 [75]2 years ago

5 0

Your answer is -1.5

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<h3>Inequalities</h3>

Inequalities is a mathematic expression that do not present equalitiy between both sides. It is represented by symbols: <, ≤, > and ≥.

For solving this exercise, firstly, you should solve the inequalities identified by letters: H, W, M, Y and C. After that, you should relate yours anwers with the options given for the exercise.

Inequality H

$-11x-4 > -15\\ \\ -11x > -15+4\\ \\ -11x > -11\; *(-1)\\ \\ 11x < 11\\ \\ x < 1$

Therefore, you should connect H with x<1.

Inequality W

$32 > -16x\\ \\ Rewriting \\ \\ -16x < 32 \\ \\ -16x < 32\; *(-1)\\ \\ 16x > -32\\ \\ x > \frac{-32}{16} \\ \\ x > -2$

Therefore, you should connect W with x>-2.

Inequality M

$3+x\leq -9\\ \\ x\leq -9-3\\ \\ x\leq -12$

Therefore, you should connect M with x≤-12.

Inequality Y

$-7x+7\leq -56\\ \\-7x\leq -56-7\\ \\ -7x\leq -63\\ \\ -7x\leq -63\; *(-1)\\ \\ 7x\geq 63\\ \\ x\geq \frac{63}{7} \\ \\ x\geq 9$

Therefore, you should connect Y with x≥9.

Inequality C

$-20\geq -5x+15\\ \\Rewriting\\ \\ 5x+15\leq -20\\ \\ -5x\leq -20-15\\ \\ -5x\leq -35\\ \\-5x\leq -35\; *(-1)\\ \\ 5x\geq 35\\ \\ x\geq \frac{35}{5} \\ \\ x\geq 7$

Therefore, you should connect C with x≥7.

Thus, the sequence is:

M - $x\leq -12$

C - $x\geq 7$

Y- $x\geq 9$

H- $x < 1$

W- $x > -2$