Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+2)& = & -11 \color{red}{+} (2+x) \\\Leftrightarrow & 6x+12& = &-11+2+x \\\Leftrightarrow & 6x \color{red}{+12} & = &-9 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &-9-12 \\\Leftrightarrow & 5x& = &-21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-3)& = & -6 \color{red}{-} (9-5x) \\\Leftrightarrow & -36x-18& = &-6-9+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &-15 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &-15+18 \\\Leftrightarrow & -41x& = &3 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{3}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-3}{41} & & \\ & V = \left\{ \frac{-3}{41} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x-5)& = & 8 \color{red}{+} (4+x) \\\Leftrightarrow & -4x-10& = &8+4+x \\\Leftrightarrow & -4x \color{red}{-10} & = &12 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &12+10 \\\Leftrightarrow & -5x& = &22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+4)& = & -11 \color{red}{-} (14+x) \\\Leftrightarrow & -24x+16& = &-11-14-x \\\Leftrightarrow & -24x \color{red}{+16} & = &-25 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &-25-16 \\\Leftrightarrow & -23x& = &-41 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-41}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{41}{23} & & \\ & V = \left\{ \frac{41}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-1)& = & 14 \color{red}{-} (9+x) \\\Leftrightarrow & -30x-5& = &14-9-x \\\Leftrightarrow & -30x \color{red}{-5} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &5+5 \\\Leftrightarrow & -29x& = &10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-10}{29} & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+3)& = & -5 \color{red}{+} (-1-3x) \\\Leftrightarrow & -4x+12& = &-5-1-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &-6 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &-6-12 \\\Leftrightarrow & -x& = &-18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-18}{ \color{red}{-1} } \\\Leftrightarrow & x = 18 & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-6)& = & -3 \color{red}{-} (7+x) \\\Leftrightarrow & 30x-36& = &-3-7-x \\\Leftrightarrow & 30x \color{red}{-36} & = &-10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &-10+36 \\\Leftrightarrow & 31x& = &26 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{26}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{26}{31} & & \\ & V = \left\{ \frac{26}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+1)& = & 10 \color{red}{+} (-5+x) \\\Leftrightarrow & 20x+4& = &10-5+x \\\Leftrightarrow & 20x \color{red}{+4} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 20x-x& = &5-4 \\\Leftrightarrow & 19x& = &1 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{1}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x+2)& = & 9 \color{red}{+} (7+x) \\\Leftrightarrow & -18x+12& = &9+7+x \\\Leftrightarrow & -18x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &16-12 \\\Leftrightarrow & -19x& = &4 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{4}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+6)& = & -6 \color{red}{-} (10+x) \\\Leftrightarrow & 8x+24& = &-6-10-x \\\Leftrightarrow & 8x \color{red}{+24} & = &-16 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 8x+x& = &-16-24 \\\Leftrightarrow & 9x& = &-40 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-40}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-40}{9} & & \\ & V = \left\{ \frac{-40}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x-4)& = & -14 \color{red}{-} (-6+x) \\\Leftrightarrow & -30x-20& = &-14+6-x \\\Leftrightarrow & -30x \color{red}{-20} & = &-8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &-8+20 \\\Leftrightarrow & -29x& = &12 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{12}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-12}{29} & & \\ & V = \left\{ \frac{-12}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+7)& = & 5 \color{red}{+} (1-3x) \\\Leftrightarrow & 4x+28& = &5+1-3x \\\Leftrightarrow & 4x \color{red}{+28} & = &6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & 4x+3x& = &6-28 \\\Leftrightarrow & 7x& = &-22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)