Question

understanding eight
read each statement and determine if it is right or wrong. if it is correct, circle the picture next to it.

1.) the expression ( 28 - 8x ) is equivalent to ( 2(14 - 2x) ).

2.) 8 is the value that could be plugged in for ( x ) to make both equations true: ( (5x + 7) div 2 = 15 ) and ( 2(x + 3) - 4 = 5(x - 1) + 7 )

3.) ( |-8 + 8| ) is equivalent to ( |-8| )

4.) 8 is one possible solution to this expression: ( \frac{3}{4}x + 2.4 < \frac{7}{16}x + 5.1 )

5.) a circle with the radius of 8 has an area greater than 100 units²

6.) the 8 in 34.008 is 100 times the value of 8 in 72.84

Explanation:

Let's analyze each statement one by one:

1. The expression \( 28 - 8x \) is equivalent to \( 2(14 - 2x) \).

• Expand \( 2(14 - 2x) \): Using the distributive property \( a(b - c)=ab - ac \), we get \( 2\times14-2\times2x = 28 - 4x \).
• \( 28 - 8x

eq28 - 4x \), so this statement is wrong.

2. \( 8 \) is the value that could be plugged in for \( x \) to make both equations \( \frac{(5x + 7)}{2}=15 \) and \( 2(x + 3)-4 = 5(x - 1)+7 \) true.

• First equation: \( \frac{(5x + 7)}{2}=15 \)
• Multiply both sides by \( 2 \): \( 5x+7 = 30 \)
• Subtract \( 7 \) from both sides: \( 5x=30 - 7=23 \)
• Divide by \( 5 \): \( x=\frac{23}{5} = 4.6

eq8 \)

• Since \( x = 8 \) does not satisfy the first equation, this statement is wrong.

3. \(|-8 + 8|\) is equivalent to \(|-8|\)

• Calculate \(|-8 + 8|\): \(|-8 + 8|=|0| = 0\)
• Calculate \(|-8|\): \(|-8| = 8\)
• \( 0

eq8 \), so this statement is wrong.

4. \( 8 \) is one possible solution to \( \frac{3}{4}x+2.4<\frac{7}{16}x + 5.1 \)

• Substitute \( x = 8 \) into the inequality:
• Left - hand side (LHS): \( \frac{3}{4}\times8+2.4=6 + 2.4=8.4 \)
• Right - hand side (RHS): \( \frac{7}{16}\times8+5.1=\frac{7}{2}+5.1 = 3.5+5.1 = 8.6 \)
• Check the inequality: \( 8.4<8.6 \), which is true. So \( x = 8 \) is a solution, and this statement is correct.

5. A circle with radius \( 8 \) has an area greater than \( 100 \) units².

• The area of a circle is given by \( A=\pi r^{2} \), with \( r = 8 \), \( A=\pi\times8^{2}=64\pi\approx64\times3.14 = 200.96 \)
• \( 200.96>100 \), so this statement is correct.

6. The \( 8 \) in \( 34.008 \) is \( 100 \) times the value of \( 8 \) in \( 72.84 \)

• The value of \( 8 \) in \( 34.008 \) is \( 0.008=\frac{8}{1000} \)
• The value of \( 8 \) in \( 72.84 \) is \( 0.8=\frac{8}{10} \)
• Check if \( 0.008 = 100\times0.8 \): \( 100\times0.8 = 80

eq0.008 \), so this statement is wrong.

Answer:

s for each statement:

1. Wrong
2. Wrong
3. Wrong
4. Correct
5. Correct
6. Wrong