Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-4x+6)=8-(8+x)\)
2. \(2(-3x+1)=15-(14+x)\)
3. \(5(4x+1)=2+(-13+3x)\)
4. \(6(2x+3)=6-(4+x)\)
5. \(2(-4x-7)=-4-(7-5x)\)
6. \(4(x-3)=1-(-9-3x)\)
7. \(2(-4x-2)=5-(10+x)\)
8. \(5(4x+7)=2+(8+x)\)
9. \(2(x-7)=-2-(2+x)\)
10. \(3(5x+3)=-7-(4+x)\)
11. \(3(-5x+2)=5-(-11+2x)\)
12. \(5(-5x-6)=-11+(4-4x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+6)& = & 8 \color{red}{-} (8+x) \\\Leftrightarrow & -8x+12& = &8-8-x \\\Leftrightarrow & -8x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &0-12 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+1)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & -6x+2& = &15-14-x \\\Leftrightarrow & -6x \color{red}{+2} & = &1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -6x+x& = &1-2 \\\Leftrightarrow & -5x& = &-1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x+1)& = & 2 \color{red}{+} (-13+3x) \\\Leftrightarrow & 20x+5& = &2-13+3x \\\Leftrightarrow & 20x \color{red}{+5} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 20x-3x& = &-11-5 \\\Leftrightarrow & 17x& = &-16 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-16}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-16}{17} & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x+3)& = & 6 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+18& = &6-4-x \\\Leftrightarrow & 12x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &2-18 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-7)& = & -4 \color{red}{-} (7-5x) \\\Leftrightarrow & -8x-14& = &-4-7+5x \\\Leftrightarrow & -8x \color{red}{-14} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+14} \\\Leftrightarrow & -8x-5x& = &-11+14 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-3)& = & 1 \color{red}{-} (-9-3x) \\\Leftrightarrow & 4x-12& = &1+9+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &10 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &10+12 \\\Leftrightarrow & x& = &22 \\ & V = \left\{ 22 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-2)& = & 5 \color{red}{-} (10+x) \\\Leftrightarrow & -8x-4& = &5-10-x \\\Leftrightarrow & -8x \color{red}{-4} & = &-5 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -8x+x& = &-5+4 \\\Leftrightarrow & -7x& = &-1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x+7)& = & 2 \color{red}{+} (8+x) \\\Leftrightarrow & 20x+35& = &2+8+x \\\Leftrightarrow & 20x \color{red}{+35} & = &10 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &10-35 \\\Leftrightarrow & 19x& = &-25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-25}{19} & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x-7)& = & -2 \color{red}{-} (2+x) \\\Leftrightarrow & 2x-14& = &-2-2-x \\\Leftrightarrow & 2x \color{red}{-14} & = &-4 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 2x+x& = &-4+14 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+3)& = & -7 \color{red}{-} (4+x) \\\Leftrightarrow & 15x+9& = &-7-4-x \\\Leftrightarrow & 15x \color{red}{+9} & = &-11 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 15x+x& = &-11-9 \\\Leftrightarrow & 16x& = &-20 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-20}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-5}{4} & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+2)& = & 5 \color{red}{-} (-11+2x) \\\Leftrightarrow & -15x+6& = &5+11-2x \\\Leftrightarrow & -15x \color{red}{+6} & = &16 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & -15x+2x& = &16-6 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x-6)& = & -11 \color{red}{+} (4-4x) \\\Leftrightarrow & -25x-30& = &-11+4-4x \\\Leftrightarrow & -25x \color{red}{-30} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & -25x+4x& = &-7+30 \\\Leftrightarrow & -21x& = &23 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{23}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-23}{21} & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)