Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+1)& = & 3 \color{red}{+} (-15+x) \\\Leftrightarrow & -9x+3& = &3-15+x \\\Leftrightarrow & -9x \color{red}{+3} & = &-12 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -9x-x& = &-12-3 \\\Leftrightarrow & -10x& = &-15 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-15}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{3}{2} & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (3x-2)& = & 7 \color{red}{-} (2-2x) \\\Leftrightarrow & 15x-10& = &7-2+2x \\\Leftrightarrow & 15x \color{red}{-10} & = &5 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 15x-2x& = &5+10 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+5)& = & -6 \color{red}{+} (12+x) \\\Leftrightarrow & -18x+15& = &-6+12+x \\\Leftrightarrow & -18x \color{red}{+15} & = &6 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -18x-x& = &6-15 \\\Leftrightarrow & -19x& = &-9 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-9}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{9}{19} & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+7)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & -20x+28& = &-13+7-x \\\Leftrightarrow & -20x \color{red}{+28} & = &-6 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -20x+x& = &-6-28 \\\Leftrightarrow & -19x& = &-34 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-34}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{34}{19} & & \\ & V = \left\{ \frac{34}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+5)& = & -11 \color{red}{-} (-5-5x) \\\Leftrightarrow & 6x+10& = &-11+5+5x \\\Leftrightarrow & 6x \color{red}{+10} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & 6x-5x& = &-6-10 \\\Leftrightarrow & x& = &-16 \\ & V = \left\{ -16 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-4)& = & 9 \color{red}{+} (12+x) \\\Leftrightarrow & -30x-20& = &9+12+x \\\Leftrightarrow & -30x \color{red}{-20} & = &21 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &21+20 \\\Leftrightarrow & -31x& = &41 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{41}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-41}{31} & & \\ & V = \left\{ \frac{-41}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-6)& = & 12 \color{red}{+} (-11+x) \\\Leftrightarrow & 20x-24& = &12-11+x \\\Leftrightarrow & 20x \color{red}{-24} & = &1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &1+24 \\\Leftrightarrow & 19x& = &25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x-7)& = & 2 \color{red}{+} (-4+x) \\\Leftrightarrow & -18x-42& = &2-4+x \\\Leftrightarrow & -18x \color{red}{-42} & = &-2 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -18x-x& = &-2+42 \\\Leftrightarrow & -19x& = &40 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{40}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-40}{19} & & \\ & V = \left\{ \frac{-40}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-2)& = & 2 \color{red}{+} (8-5x) \\\Leftrightarrow & 6x-6& = &2+8-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &10 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &10+6 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-6)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x-24& = &-14-9+x \\\Leftrightarrow & 12x \color{red}{-24} & = &-23 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &-23+24 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x-3)& = & 3 \color{red}{+} (-10+3x) \\\Leftrightarrow & -10x-6& = &3-10+3x \\\Leftrightarrow & -10x \color{red}{-6} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -10x-3x& = &-7+6 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-7)& = & 1 \color{red}{-} (-2+x) \\\Leftrightarrow & -10x-35& = &1+2-x \\\Leftrightarrow & -10x \color{red}{-35} & = &3 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -10x+x& = &3+35 \\\Leftrightarrow & -9x& = &38 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{38}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-38}{9} & & \\ & V = \left\{ \frac{-38}{9} \right\} & \\\end{align}\)