Solve inequality algebraically x + 6 x + 1 ≥ 2 , x ≠ - 1

We have to solve inequality algebraically x + 6 x + 1 ≥ 2 , x ≠ 1 Rearrange and simplify x + 6 x + 1 - 2 ≥ 0 ⇒ x + 6 - 2 x - 2 x + 1 ≥ 0 ⇒ 4 - x x + 1 ≥ 0 Case 1 : 4 - x < 0 and x + 1 < 0 Then x > 4 and x < - 1 . Case 2 : 4 - x > 0 and x + 1 > 0 Then x < 4 and x > - 1 . Solution is − 1 < x ≤ 4

Solve inequality algebraically x + 6 x + 1 ≥ 2 , x ≠ - 1

We have to solve inequality algebraically x + 6 x + 1 ≥ 2 , x ≠ 1 Rearrange and simplify x + 6 x + 1 - 2 ≥ 0 ⇒ x + 6 - 2 x - 2 x + 1 ≥ 0 ⇒ 4 - x x + 1 ≥ 0 Case 1 : 4 - x < 0 and x + 1 < 0 Then x > 4 and x < - 1 . Case 2 : 4 - x > 0 and x + 1 > 0 Then x < 4 and x > - 1 . Solution is − 1 < x ≤ 4

Solve inequality algebraically x + 1 x - 4 > 0 , x ≠ 4

We have to solve inequality algebraically 1 + x x - 4 > 0 , x ≠ 4 Case 1 : 1 + x < 0 and x - 4 > 0 Then x < - 1 and x > 4 . Case 2 : 1 + x > 0 and x - 4 < 0 Then x > - 1 and x < 4 . Solution is x < − 1 or x > 4 .

Solve inequality algebraically 8 - x x - 2 ≤ 5 , x ≠ 2

We have to solve inequality algebraically 8 - x x - 2 ≤ 5 , x ≠ 2 Rearrange and simplify 8 - x x - 2 - 5 ≤ 0 ⇒ 8 - x - 5 x + 10 x - 2 ≤ 0 ⇒ - 6 x + 18 x - 2 ≤ 0 Case 1 : - 6 x + 18 ≤ 0 and x - 2 > 0 Then x ≥ 3 and x > 2 . hence x ≥ 3 Case 2 : - 6 x + 18 ≥ 0 and x - 2 < 0 Then x ≤ 3 and x < 2 . hence x < 2 Solution is x < 2 or x ≥ 3

Solve inequality algebraically 3 + x x + 1 < 0 , x ≠ 0

We have to solve inequality algebraically and check solution graphically 3 + x x + 1 < 0 , x ≠ 0 Rearrange and simplify 3 + x + x x < 0 ⇒ 3 + 2 x x < 0 Case 1 : 3 + 2 x < 0 and x > 0 Then x < - 3 2 and x < 0 . Case 2 : 3 + 2 x > 0 and x < 0 Then x > - 3 2 and x < 0 . Solution is − 3 2 < x < 0 .

Solve inequality algebraically 5 x - 8 x - 5 ≥ 2 , x ≠ 5

We have to solve inequality algebraically 5 x - 8 x - 5 ≥ 2 , x ≠ 5 Rearrange and simplify 5 x - 8 x - 5 - 2 ≥ 0 ⇒ 5 x - 8 - 2 x + 10 x - 5 ≥ 0 ⇒ 3 x + 2 x - 5 ≥ 0 Case 1 : 3 x + 2 ≤ 0 and x - 5 < 0 Then x ≤ - 2 3 and x < 5 . Case 2 : 3 x + 2 ≥ 0 and x - 5 > 0 Then x ≥ - 2 3 and x > 5 . Solution is x ≤ − 2 3 or x > 5

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 1

EASY

MYP:4-5

IMPORTANT

Earn 100

Solve inequality algebraically $\frac{x + 6}{x + 1} \geq 2, x \neq - 1$

Important Questions on Non-Linear Inequalities

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 1

Solve inequality algebraically $\frac{x + 1}{x - 4} > 0, x \neq 4$

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 1

Solve inequality algebraically

$\frac{8 - x}{x - 2} \leq 5, x \neq 2$

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 1

Solve inequality algebraically

$\frac{3 + x}{x} + 1 < 0, x \neq 0$

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 1

Solve inequality algebraically

$\frac{5 x - 8}{x - 5} \geq 2, x \neq 5$

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 2

Determine the range of values that a variable $x$ can take such that adding to the numerator and denominator of the fraction $\frac{2}{3}$ results in a fraction that is less than $\frac{1}{2}$ .

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Practice 6>Q 3

Gretchen would like to improve her free throw average in basketball. She has scored $9$ free throws in her first $20$ trials. Determine how many more consecutive free throws she would need to successfully make in order to bring her average up to $70 %$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Mixed practice>Q 1

Solve the following inequality graphically, giving exact answers or accurate to $3$ significant figures,

${(x + 2)}^{2} > 1$

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 17 - Non-Linear Inequalities>Mixed practice>Q 1

Solve the following inequality graphically, giving exact answers or accurate to $3$ significant figures,

$x^{2} - 3 x - 1 \geq - 11 x + 4$