Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x-4)& = & -8 \color{red}{+} (1+x) \\\Leftrightarrow & 10x-8& = &-8+1+x \\\Leftrightarrow & 10x \color{red}{-8} & = &-7 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 10x-x& = &-7+8 \\\Leftrightarrow & 9x& = &1 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{1}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x-2)& = & -1 \color{red}{+} (-3-4x) \\\Leftrightarrow & -25x-10& = &-1-3-4x \\\Leftrightarrow & -25x \color{red}{-10} & = &-4 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & -25x+4x& = &-4+10 \\\Leftrightarrow & -21x& = &6 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{6}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x+5)& = & -2 \color{red}{-} (12+5x) \\\Leftrightarrow & -12x+30& = &-2-12-5x \\\Leftrightarrow & -12x \color{red}{+30} & = &-14 \color{red}{-5x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -12x+5x& = &-14-30 \\\Leftrightarrow & -7x& = &-44 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-44}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{44}{7} & & \\ & V = \left\{ \frac{44}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x+5)& = & -12 \color{red}{+} (-7+5x) \\\Leftrightarrow & -18x+30& = &-12-7+5x \\\Leftrightarrow & -18x \color{red}{+30} & = &-19 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & -18x-5x& = &-19-30 \\\Leftrightarrow & -23x& = &-49 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-49}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{49}{23} & & \\ & V = \left\{ \frac{49}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+5)& = & -11 \color{red}{-} (-3+5x) \\\Leftrightarrow & 6x+10& = &-11+3-5x \\\Leftrightarrow & 6x \color{red}{+10} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-10} \\\Leftrightarrow & 6x+5x& = &-8-10 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-4)& = & 5 \color{red}{-} (4+5x) \\\Leftrightarrow & -6x-24& = &5-4-5x \\\Leftrightarrow & -6x \color{red}{-24} & = &1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -6x+5x& = &1+24 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-7)& = & 14 \color{red}{-} (3+5x) \\\Leftrightarrow & 6x-42& = &14-3-5x \\\Leftrightarrow & 6x \color{red}{-42} & = &11 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 6x+5x& = &11+42 \\\Leftrightarrow & 11x& = &53 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{53}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{53}{11} & & \\ & V = \left\{ \frac{53}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x-7)& = & 8 \color{red}{+} (10+3x) \\\Leftrightarrow & 10x-35& = &8+10+3x \\\Leftrightarrow & 10x \color{red}{-35} & = &18 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 10x-3x& = &18+35 \\\Leftrightarrow & 7x& = &53 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{53}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{53}{7} & & \\ & V = \left\{ \frac{53}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x-7)& = & -12 \color{red}{+} (2+3x) \\\Leftrightarrow & 2x-14& = &-12+2+3x \\\Leftrightarrow & 2x \color{red}{-14} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & 2x-3x& = &-10+14 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x+5)& = & -8 \color{red}{+} (14+x) \\\Leftrightarrow & -20x+20& = &-8+14+x \\\Leftrightarrow & -20x \color{red}{+20} & = &6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &6-20 \\\Leftrightarrow & -21x& = &-14 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-14}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x+4)& = & -3 \color{red}{-} (-13-2x) \\\Leftrightarrow & -5x+20& = &-3+13+2x \\\Leftrightarrow & -5x \color{red}{+20} & = &10 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -5x-2x& = &10-20 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-2)& = & 14 \color{red}{-} (-14+3x) \\\Leftrightarrow & -4x-4& = &14+14-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &28 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &28 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &28+4 \\\Leftrightarrow & -x& = &32 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{32}{ \color{red}{-1} } \\\Leftrightarrow & x = -32 & & \\ & V = \left\{ -32 \right\} & \\\end{align}\)