Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x+5)& = & 9 \color{red}{+} (-2+x) \\\Leftrightarrow & -20x+20& = &9-2+x \\\Leftrightarrow & -20x \color{red}{+20} & = &7 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &7-20 \\\Leftrightarrow & -21x& = &-13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-7)& = & -4 \color{red}{-} (-8+3x) \\\Leftrightarrow & -4x-28& = &-4+8-3x \\\Leftrightarrow & -4x \color{red}{-28} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -4x+3x& = &4+28 \\\Leftrightarrow & -x& = &32 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{32}{ \color{red}{-1} } \\\Leftrightarrow & x = -32 & & \\ & V = \left\{ -32 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-6)& = & -8 \color{red}{+} (-10-4x) \\\Leftrightarrow & -9x-18& = &-8-10-4x \\\Leftrightarrow & -9x \color{red}{-18} & = &-18 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &-18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & -9x+4x& = &-18+18 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+1)& = & 2 \color{red}{+} (-12+x) \\\Leftrightarrow & 9x+3& = &2-12+x \\\Leftrightarrow & 9x \color{red}{+3} & = &-10 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 9x-x& = &-10-3 \\\Leftrightarrow & 8x& = &-13 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-13}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-13}{8} & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-5)& = & -8 \color{red}{+} (15+x) \\\Leftrightarrow & -6x-15& = &-8+15+x \\\Leftrightarrow & -6x \color{red}{-15} & = &7 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &7+15 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x+4)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & -18x+24& = &-15+6+x \\\Leftrightarrow & -18x \color{red}{+24} & = &-9 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -18x-x& = &-9-24 \\\Leftrightarrow & -19x& = &-33 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-33}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{33}{19} & & \\ & V = \left\{ \frac{33}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x+2)& = & 12 \color{red}{+} (-4+x) \\\Leftrightarrow & 2x+4& = &12-4+x \\\Leftrightarrow & 2x \color{red}{+4} & = &8 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 2x-x& = &8-4 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+4)& = & -1 \color{red}{-} (-2+x) \\\Leftrightarrow & 18x+12& = &-1+2-x \\\Leftrightarrow & 18x \color{red}{+12} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &1-12 \\\Leftrightarrow & 19x& = &-11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+3)& = & -15 \color{red}{-} (-7-4x) \\\Leftrightarrow & 9x+9& = &-15+7+4x \\\Leftrightarrow & 9x \color{red}{+9} & = &-8 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & 9x-4x& = &-8-9 \\\Leftrightarrow & 5x& = &-17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x-5)& = & 12 \color{red}{-} (-4-3x) \\\Leftrightarrow & 10x-10& = &12+4+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &16 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &16+10 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x-3)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & -30x-15& = &14-14-x \\\Leftrightarrow & -30x \color{red}{-15} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -30x+x& = &0+15 \\\Leftrightarrow & -29x& = &15 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{15}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-15}{29} & & \\ & V = \left\{ \frac{-15}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+6)& = & 7 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+36& = &7-12-x \\\Leftrightarrow & -24x \color{red}{+36} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -24x+x& = &-5-36 \\\Leftrightarrow & -23x& = &-41 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-41}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{41}{23} & & \\ & V = \left\{ \frac{41}{23} \right\} & \\\end{align}\)