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3 years ago

Graph the solution to this inequality on the number line. −1/3x + 1/2 ≥ −3/4

Mathematics

1 answer:

valentina_108 [34]3 years ago

7 0

Answer:

4.5 (4.5 units to the left of 0) Make sure to draw a solid dot over 4.5 and an arrow pointing in the right direction.

>= is the greater than or equal to symbol

Step-by-step explanation

1. Combine like terms- In this problem, the like terms are 1/2 and -3/4, so to move 1/2 over to the other side of the equation, we have to divide each side by 2/1, which is the same as multiplying each side by 2: -1/3x + 1/2 * 2 >= -3/4 * 2.

2. Separate the fraction from x- Now, we simply divide each side by -3/1, which is the same as multiplying each side as -3: -1/3x * -3 >= -3/2 * -3

3. Graph on the number line- We've found that x = 4.5. To check, substitute in 4.5 for the value of x: -1/3(4.5) + 1/2 >= -3/4. -1 >= -3/4 is a true inequality. To graph it on the number line, draw a solid dot over 4.5 and an arrow in the direction of the righthand side.

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Which graph shows the solution to the system of linear inequalities? y< 2x-5 y>-3x + 1

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Answer:

See explanation

Step-by-step explanation:

Plot the solution sets to both inequalities.

1. For the inequality $y$ First, plot the dotted line $y=2x+5$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$2\cdot 0-5=-5$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

2. For the inequality $y>-3x+1.$ First, plot the dotted line $y=-3x+1$ (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.

$-3\cdot 0+1=1>0$

so the origin does not belong to the needed part. Shade the part, which does not include origin.

3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.

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3 years ago

Find the slope of the line (18,0)(10,-5)

Leya [2.2K]

Answer:

$m=\frac{5}{8}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (18, 0)

Point (10, -5)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]: $m=\frac{-5-0}{10-18}$
Subtract: $m=\frac{-5}{-8}$
Simplify: $m=\frac{5}{8}$

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