Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+3)& = & -8 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x+18& = &-8+13-5x \\\Leftrightarrow & 6x \color{red}{+18} & = &5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 6x+5x& = &5-18 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-5)& = & 12 \color{red}{-} (-5+x) \\\Leftrightarrow & 3x-15& = &12+5-x \\\Leftrightarrow & 3x \color{red}{-15} & = &17 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 3x+x& = &17+15 \\\Leftrightarrow & 4x& = &32 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{32}{ \color{red}{4} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-6)& = & -5 \color{red}{-} (1+x) \\\Leftrightarrow & -2x-12& = &-5-1-x \\\Leftrightarrow & -2x \color{red}{-12} & = &-6 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -2x+x& = &-6+12 \\\Leftrightarrow & -x& = &6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{6}{ \color{red}{-1} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x-4)& = & -11 \color{red}{+} (-14+x) \\\Leftrightarrow & -4x-16& = &-11-14+x \\\Leftrightarrow & -4x \color{red}{-16} & = &-25 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &-25+16 \\\Leftrightarrow & -5x& = &-9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-2)& = & -7 \color{red}{+} (11+x) \\\Leftrightarrow & -18x-6& = &-7+11+x \\\Leftrightarrow & -18x \color{red}{-6} & = &4 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &4+6 \\\Leftrightarrow & -19x& = &10 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{10}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-10}{19} & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x-1)& = & 3 \color{red}{-} (-4-5x) \\\Leftrightarrow & -18x-3& = &3+4+5x \\\Leftrightarrow & -18x \color{red}{-3} & = &7 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -18x-5x& = &7+3 \\\Leftrightarrow & -23x& = &10 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{10}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-10}{23} & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x+4)& = & -5 \color{red}{-} (1+x) \\\Leftrightarrow & 24x+24& = &-5-1-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-6-24 \\\Leftrightarrow & 25x& = &-30 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-30}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x+2)& = & -14 \color{red}{-} (6+4x) \\\Leftrightarrow & -25x+10& = &-14-6-4x \\\Leftrightarrow & -25x \color{red}{+10} & = &-20 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &-20 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & -25x+4x& = &-20-10 \\\Leftrightarrow & -21x& = &-30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-3)& = & -12 \color{red}{-} (3+x) \\\Leftrightarrow & -12x-6& = &-12-3-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-15+6 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x+5)& = & 14 \color{red}{+} (-9+x) \\\Leftrightarrow & 8x+20& = &14-9+x \\\Leftrightarrow & 8x \color{red}{+20} & = &5 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 8x-x& = &5-20 \\\Leftrightarrow & 7x& = &-15 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-15}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x+3)& = & 7 \color{red}{+} (10+x) \\\Leftrightarrow & -9x+9& = &7+10+x \\\Leftrightarrow & -9x \color{red}{+9} & = &17 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -9x-x& = &17-9 \\\Leftrightarrow & -10x& = &8 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{8}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x-7)& = & -1 \color{red}{-} (4+x) \\\Leftrightarrow & -6x-21& = &-1-4-x \\\Leftrightarrow & -6x \color{red}{-21} & = &-5 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -6x+x& = &-5+21 \\\Leftrightarrow & -5x& = &16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)