Solutions for Expressions, Equations, and Inequalities

Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!

Expression Calculation:

(22−3)+369∙2−4(2^2 – 3) + \frac{36}{9} \bullet 2 – 4(22−3)+936​∙2−4

Step 1: Exponentiation (2² = 4)

(4−3)+369∙2−4(4 – 3) + \frac{36}{9} \bullet 2 – 4(4−3)+936​∙2−4

(Operation: exponentiation)

Step 2: Subtraction (4 – 3 = 1)

1+369∙2−41 + \frac{36}{9} \bullet 2 – 41+936​∙2−4

(Operation: subtraction)

Step 3: Division (36 ÷ 9 = 4)

$$1+4\bullet 2-4$$

(Operation: division)

Step 4: Multiplication (4 × 2 = 8)

$$1+8-4$$

(Operation: multiplication)

Step 5: Addition (1 + 8 = 9)

$$9-4$$

(Operation: addition)

Step 6: Subtraction (9 – 4 = 5)

$$5$$

(Operation: subtraction)

Solving for x in the equation:

$$2(5x-4)+x=3(x+1)-7$$

Step 1: Distribute

$$10x-8+x=3x+3-7$$

(Operation: distributive property)

Step 2: Combine Like Terms

$$11x-8=3x-4$$

(Operation: combining like terms)

Step 3: Move 3x to the left side (subtract 3x from both sides)

$$11x-3x-8=-4$$ $$8x-8=-4$$

(Operation: subtraction)

Step 4: Move -8 to the right side (add 8 to both sides)

$$8x=4$$

(Operation: addition)

Step 5: Solve for x (divide by 8)

x=48=12x = \frac{4}{8} = \frac{1}{2}x=84​=21​

(Operation: division)

x=12\mathbf{x = \frac{1}{2}}x=21​

Solving the Inequality:

13x+25<56\frac{1}{3}x + \frac{2}{5} < \frac{5}{6}31​x+52​<65​

Step 1: Subtract 25\frac{2}{5}52​ from both sides

13x<56−25\frac{1}{3}x < \frac{5}{6} – \frac{2}{5}31​x<65​−52​

Step 2: Find a Common Denominator (LCD = 30)

Convert fractions:

56=2530,25=1230\frac{5}{6} = \frac{25}{30}, \quad \frac{2}{5} = \frac{12}{30}65​=3025​,52​=3012​

Subtract:

2530−1230=1330\frac{25}{30} – \frac{12}{30} = \frac{13}{30}3025​−3012​=3013​ 13x<1330\frac{1}{3}x < \frac{13}{30}31​x<3013​

Step 3: Multiply both sides by 3 to isolate x

x<1330×3x < \frac{13}{30} \times 3x<3013​×3 x<3930x < \frac{39}{30}x<3039​

Step 4: Simplify

x<1310x < \frac{13}{10}x<1013​

or

$$x<1.3$$ x<1310 or x<1.3\mathbf{x < \frac{13}{10} \text{ or } x < 1.3}x<1013​ or x<1.3