Translate the difference of \(15\) and \(x\) is \(12\) into symbols.

Translate the product of \(6\) and \(a\) is \(30\) into symbols.

Simplify: \(10+2(7-3)-4^2\)

Simplify: \(15+24\div 6-3^2\)

Name the property that justifies the equation. \[4(2y)=(4\cdot 2)y\]

Name the property that justifies the equation. \[5(x-3)=5x-15\]

Name the property that justifies the equation. \[4+x=x+4\]

Name the property that justifies the equation. \[(a+5)-2=a+(5-2)\]

Simplify: \(-2(3)-7\)

Simplify: \(\;2(3)^3-4(-2)^4\)

Simplify: \(\;9+4(2-6)\)

Simplify: \(\;5-3[-2(1+4)+3(-3)]\)

Simplify: \(\;\displaystyle\frac{-4(3)+5(-2)}{-5-6}\)

Simplify: \(\;\displaystyle\frac{4(3-5)-2(-6+8)}{4(-2)+10}\)

Apply the associative property, and then simplify. \[5+(7+3x)\]

Apply the associative property, and then simplify. \[3(-5y)\]

Multiply by applying the distributive property. \[-5(2x-3)\]

Multiply by applying the distributive property. \[\displaystyle\frac{1}{3}(6x+12)\]

Factor \(660\) into the product of primes.

Factor \(4,725\) into the product of primes.

Combine. \(\displaystyle\frac{5}{24}+\displaystyle\frac{9}{36}\)

Combine. \(\displaystyle\frac{5}{y}+\displaystyle\frac{6}{y}\)

Write the sum of \(6\) and \(-9\) in symbols, and then simplify it.

Write the difference of \(-5\) and \(-12\) in symbols, and then simplify it.

Write the product of \(6\) and \(-7\) in symbols, and then simplify it.

Write the quotient of \(31\) and \(-8\) in symbols, and then simplify it.

Mini Lecture

1. Write \(\displaystyle\frac{5}{8}\) as a fraction with a denominator of \(24\).

2. Give the opposite, reciprocal, and absolute value for \(-3\).

3. Insert \(<\) or \(>\) between \(-3\) and \(-7\).

4. Simplify: \(10-|7-2(5-3)|\).

5. Multiply \(\displaystyle\frac{1}{2}(3)\)

6. Multiply \(3\cdot \displaystyle\frac{1}{3}\)

Simplify \(5(4x)\) by using the associative property.

Simplify \(\dfrac{1}{4}(4a)\) by using the associative property.

Apply the distributive property to \(\dfrac{1}{2}(3x+6)\) and then simplify the result.

Simplify: \(\,2(3y+4)+2\)

Apply the distributive property to \(a\left(1+\dfrac{1}{a}\right)\) and then simplify the result.

Apply the distributive property to \(3\left(\dfrac{1}{3}x+5\right)\) and then simplify the result.

Apply the distributive property to \(6\left(\dfrac{1}{3}x+\dfrac{1}{2}y\right)\) and then simplify the result.

Use the distributive property to combine similar terms for the expression \(3x+5x\).

Use the distributive property to combine similar terms for the expression \(3y+y\)

Simplify: \(7x+4+6x+3\)

Simplify: \(4+3(2y+5)+8y\)

1. \(7(1)=7\)

2. \(4+(-4)=0\)

3. \(6\left(\dfrac{1}{6}\right)=1\)

4. \((5+0)+2=5+2\)

Mini Lecture
Apply the associative property.

1. \((x+2)+7\)

2. \(9(6y)\)

3. \(\displaystyle\frac{1}{3}(3x)\)

Apply the distributive property.

4. \(8(x-2)\)

5. \(2(3a+7)\)

6. \(7(x+4)+10\)

1. \(5-3\)

2. \(-7-6\)

3. \(9-(-2)\)

4. \(-6-(-5)\)

Simplify \((-2-3)(5-9)\)

Simplify \(2-5(7-4)-6\)

Simplify: \(\dfrac{-8-8}{-5-3}\)

Simplify: \(\dfrac{-5(-4)+2(-3)}{2(-1)-5}\)

Simplify: \(3(2y-1)+y\)

Simplify: \(8-3(4x-2)+5x\)

Simplify: \(5(2a+3)-(6a-4)\)

Mini Lecture
Simplify.

1. \(-7-3\)

2. \(-7-(-3)\)

3. \(3(-4)+2\)

4. \(2-5(-4-6)\)

5. \(2(-3)^2-4(-2)^3\)

6. \(5(3y+1)-(8y-5)\)

Mini Lecture
Add.

1. \(13+(-20)\)

2. \(-6+3\)

3. \(-6+(-6)\)

Simplify.

4. \(5+(-6)+(-7)\)

5. \((-9+2)+\left[5+(-8)\right]+(-4)\)

Apply the quotient property for exponents to each expression, and then simplify the result. All answers that contain exponents should contain positive exponents only.

Simplify: \(\; 5+3(2+4)\)

Mini Lecture
Simplify.

1. \(x^5\cdot x^4\)

2. \(\left(2^3\right)^2\)

3. \(-3a^2\left(2a^4\right)\)

4. \(3^{-2}\)

5. \(\left(3y^5\right)^{-2}\left(2y^{-4}\right)^3\)

6. \(\dfrac{\left(6x^{-3}y^{-5}\right)^2}{\left(3x^{-4}y^{-3}\right)^4}\)

7. Write \(378,000\) in scientific notation.

8. Write \(3.44\times 10^{-3}\) in expanded form.