All categories

3 years ago

Solve the inequality 2x - 3 < x 2 ≤ 3x 5. show your work

2 answers:

8 0

2x − 3 < x + 2 
∴ x − 3 < 2 
∴ x < 5 

x + 2 ≤ 3x + 5 
∴ 2 ≤ 2x + 5 
∴ -3 ≤ 2x 
∴ -3/2 ≤ x 

-3/2 ≤ x < 5

Alexxx [7]3 years ago

3 0

Answer:

-3/2 ≤ x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x+5

Solve the inequality separately

2x-3 <x+2 and x+2≤ 3x+5

LEts solve one by one

2x-3 <x+2

Subtract x from both sides

x -3 < 2

add 3 on both sides

x< 5

x+2≤ 3x+5

Subtract 3x from both sides

-2x + 2 ≤ 5

Subtract 2 from both sides

-2x ≤ 3

Divide both sides by -2

x ≥ -3/2

we got x>= -3/2 and x<5

so x lies between -3/2 and 5

-3/2 ≤ x < 5

You might be interested in

Write an equation in slope - intercept form for the line that satisfies each set of conditions

ivanzaharov [21]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(1)

Rearrange 3x + 2y = 1 into this form by subtracting 3x from both sides

2y = - 3x + 1 ( divide all terms by 2 )

y = - $\frac{3}{2}$ x + $\frac{1}{2}$ ← in slope- intercept form

with slope m = - $\frac{3}{2}$

Parallel lines have equal slopes, thus

y = - $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute (- 6, 15) into the partial equation

15 = 9 + c ⇒ c = 15 - 9 = 6

y = - $\frac{3}{2}$ x + 6 ← equation of line

(2)

Rearrange x + 2y = 8 into slope- intercept form by subtracting x from both sides

2y = - x + 8 ( divide all terms by 2 )

y = - $\frac{1}{2}$ x + 4 ← in slope- intercept form

with slope m = - $\frac{1}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{1}{2} }$ = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (5, - 2) into the partial equation

- 2 = 10 + c ⇒ c = - 2 - 10 = - 12

y = 2x - 12 ← equation of line

3 0

2 years ago

Read 2 more answers

The sum of 9and -16 increased by 4

LenaWriter [7]

Answer:

-3

Step-by-step explanation:

The statement is,

→ Sum of 9 and -16 increased by 4

The equation will be,

→ {9 +(-16)} + 4

→ (9 - 16) + 4

→ -7 + 4

→ [ -3 ]

Hence, the solution is -3.

7 0

1 year ago

the amount of interest earned in a savings account varies directly with the amount of maney saved. if $126 in intrest is earned

Mashcka [7]

2,000 + 1,000 = 3,00 so you would have $2,000 more to get to 3,000

3 0

2 years ago

3. Baskin Robbins has a new 3-gallon container of

Lynna [10]

2 gallons were left at the end of the day

3 0

2 years ago

HELP, I’M STUCK !

vaieri [72.5K]

Since P(X = x) = 0.3 for all 0 ≤ x ≤ α, we have

$\displaystyle\int_{-\infty}^\infty P(X=x)\,\mathrm dx=1\implies0.3\int_0^\alpha\mathrm dx=0.3\alpha=1\implies\alpha=\dfrac{10}3$

So,

$P(X>2) = \displaystyle\int_2^\infty P(X=x)\,\mathrm dx=0.3\int_2^{\frac{10}3}\mathrm dx$

$P(X>2)=0.3\left(\dfrac{10}3-2\right)=\boxed{\dfrac25}$

6 0

2 years ago