Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x-7)& = & 13 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-21& = &13-6+x \\\Leftrightarrow & 6x \color{red}{-21} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 6x-x& = &7+21 \\\Leftrightarrow & 5x& = &28 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{28}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{28}{5} & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x+2)& = & 14 \color{red}{+} (-9-5x) \\\Leftrightarrow & -3x+6& = &14-9-5x \\\Leftrightarrow & -3x \color{red}{+6} & = &5 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -3x+5x& = &5-6 \\\Leftrightarrow & 2x& = &-1 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-1}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x+4)& = & 5 \color{red}{-} (13-5x) \\\Leftrightarrow & -18x+24& = &5-13+5x \\\Leftrightarrow & -18x \color{red}{+24} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -18x-5x& = &-8-24 \\\Leftrightarrow & -23x& = &-32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x+2)& = & -9 \color{red}{+} (7-3x) \\\Leftrightarrow & 10x+4& = &-9+7-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &-2-4 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x+2)& = & 12 \color{red}{-} (-3+x) \\\Leftrightarrow & -30x+10& = &12+3-x \\\Leftrightarrow & -30x \color{red}{+10} & = &15 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -30x+x& = &15-10 \\\Leftrightarrow & -29x& = &5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-5}{29} & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x+3)& = & -13 \color{red}{-} (-12-5x) \\\Leftrightarrow & -16x+12& = &-13+12+5x \\\Leftrightarrow & -16x \color{red}{+12} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -16x-5x& = &-1-12 \\\Leftrightarrow & -21x& = &-13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-4)& = & -14 \color{red}{-} (10+x) \\\Leftrightarrow & 8x-16& = &-14-10-x \\\Leftrightarrow & 8x \color{red}{-16} & = &-24 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 8x+x& = &-24+16 \\\Leftrightarrow & 9x& = &-8 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-8}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-1)& = & 2 \color{red}{+} (-10+x) \\\Leftrightarrow & -36x-6& = &2-10+x \\\Leftrightarrow & -36x \color{red}{-6} & = &-8 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -36x-x& = &-8+6 \\\Leftrightarrow & -37x& = &-2 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-2}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{2}{37} & & \\ & V = \left\{ \frac{2}{37} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+3)& = & 1 \color{red}{+} (3+3x) \\\Leftrightarrow & -10x+6& = &1+3+3x \\\Leftrightarrow & -10x \color{red}{+6} & = &4 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -10x-3x& = &4-6 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x-1)& = & 3 \color{red}{+} (2-3x) \\\Leftrightarrow & 4x-4& = &3+2-3x \\\Leftrightarrow & 4x \color{red}{-4} & = &5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 4x+3x& = &5+4 \\\Leftrightarrow & 7x& = &9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-3)& = & -9 \color{red}{+} (-15+x) \\\Leftrightarrow & -24x-18& = &-9-15+x \\\Leftrightarrow & -24x \color{red}{-18} & = &-24 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &-24+18 \\\Leftrightarrow & -25x& = &-6 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-6}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+7)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & 20x+28& = &-15+6+x \\\Leftrightarrow & 20x \color{red}{+28} & = &-9 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 20x-x& = &-9-28 \\\Leftrightarrow & 19x& = &-37 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-37}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-37}{19} & & \\ & V = \left\{ \frac{-37}{19} \right\} & \\\end{align}\)