[math]4x=\text{-}28[/math]
[math]x-\text{-}6=\text{-}2[/math]
[math]\text{-}x+4=\text{-}9[/math]
[math]\text{-}3x+7=1[/math]
[math]25x+\text{-}11=\text{-}86[/math]
Here is an equation [math]2x+9=\text{-}15[/math]. Write three different equations that have the same solution as [math]2x+9=\text{-}15[/math]. Show or explain how you found them.
Select [b]all [/b]the equations that match the diagram.[br][img]data:image/png;base64,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[/img]
What unknown amounts can be found by using the diagram or reasoning about the situation?
A stack of nested paper cups is 8 inches tall. The first cup is 4 inches tall and each of the rest of the cups in the stack adds [math]\frac{1}{4}[/math] inch to the height of the stack.
A baker uses 4 cups of flour. She uses [math]\frac{1}{4}[/math] cups to flour the counters and the rest to make 8 identical muffins.
Elena has an 8-foot piece of ribbon. She cuts off a piece that is [math]\frac{1}{4}[/math] of a foot long and cuts the remainder into four pieces of equal length.