Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+3)& = & -15 \color{red}{-} (6-3x) \\\Leftrightarrow & 4x+6& = &-15-6+3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-21 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 4x-3x& = &-21-6 \\\Leftrightarrow & x& = &-27 \\ & V = \left\{ -27 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+1)& = & 6 \color{red}{+} (3-2x) \\\Leftrightarrow & 25x+5& = &6+3-2x \\\Leftrightarrow & 25x \color{red}{+5} & = &9 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & 25x+2x& = &9-5 \\\Leftrightarrow & 27x& = &4 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{4}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{4}{27} & & \\ & V = \left\{ \frac{4}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x+6)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & 4x+12& = &-11-11-x \\\Leftrightarrow & 4x \color{red}{+12} & = &-22 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 4x+x& = &-22-12 \\\Leftrightarrow & 5x& = &-34 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-34}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-34}{5} & & \\ & V = \left\{ \frac{-34}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x+4)& = & 8 \color{red}{-} (11+x) \\\Leftrightarrow & 18x+24& = &8-11-x \\\Leftrightarrow & 18x \color{red}{+24} & = &-3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 18x+x& = &-3-24 \\\Leftrightarrow & 19x& = &-27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-7)& = & -15 \color{red}{-} (-7-5x) \\\Leftrightarrow & -18x-42& = &-15+7+5x \\\Leftrightarrow & -18x \color{red}{-42} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & -18x-5x& = &-8+42 \\\Leftrightarrow & -23x& = &34 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{34}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-34}{23} & & \\ & V = \left\{ \frac{-34}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+4)& = & -12 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x+12& = &-12+9-x \\\Leftrightarrow & 12x \color{red}{+12} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &-3-12 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x-7)& = & -7 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x-42& = &-7+10-x \\\Leftrightarrow & 12x \color{red}{-42} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 12x+x& = &3+42 \\\Leftrightarrow & 13x& = &45 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{45}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{45}{13} & & \\ & V = \left\{ \frac{45}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-7)& = & -12 \color{red}{+} (4+x) \\\Leftrightarrow & -6x-21& = &-12+4+x \\\Leftrightarrow & -6x \color{red}{-21} & = &-8 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -6x-x& = &-8+21 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x+2)& = & -9 \color{red}{-} (5-5x) \\\Leftrightarrow & -6x+12& = &-9-5+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-14 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &-14-12 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-6)& = & 14 \color{red}{+} (-7+3x) \\\Leftrightarrow & -16x-24& = &14-7+3x \\\Leftrightarrow & -16x \color{red}{-24} & = &7 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -16x-3x& = &7+24 \\\Leftrightarrow & -19x& = &31 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{31}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-31}{19} & & \\ & V = \left\{ \frac{-31}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-7)& = & -8 \color{red}{-} (13+3x) \\\Leftrightarrow & -20x-28& = &-8-13-3x \\\Leftrightarrow & -20x \color{red}{-28} & = &-21 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -20x+3x& = &-21+28 \\\Leftrightarrow & -17x& = &7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-7}{17} & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-3)& = & -3 \color{red}{+} (5-3x) \\\Leftrightarrow & -16x-12& = &-3+5-3x \\\Leftrightarrow & -16x \color{red}{-12} & = &2 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -16x+3x& = &2+12 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)