Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+1)& = & -3 \color{red}{-} (7-2x) \\\Leftrightarrow & -3x+3& = &-3-7+2x \\\Leftrightarrow & -3x \color{red}{+3} & = &-10 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -3x-2x& = &-10-3 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x+3)& = & -2 \color{red}{-} (9-2x) \\\Leftrightarrow & -25x+15& = &-2-9+2x \\\Leftrightarrow & -25x \color{red}{+15} & = &-11 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -25x-2x& = &-11-15 \\\Leftrightarrow & -27x& = &-26 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-26}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{26}{27} & & \\ & V = \left\{ \frac{26}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-5)& = & -7 \color{red}{+} (-2+4x) \\\Leftrightarrow & 15x-25& = &-7-2+4x \\\Leftrightarrow & 15x \color{red}{-25} & = &-9 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &-9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & 15x-4x& = &-9+25 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x-2)& = & 2 \color{red}{-} (-10-5x) \\\Leftrightarrow & -6x-6& = &2+10+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &12 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &12+6 \\\Leftrightarrow & -11x& = &18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x+7)& = & -14 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x+42& = &-14+9-x \\\Leftrightarrow & -30x \color{red}{+42} & = &-5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &-5-42 \\\Leftrightarrow & -29x& = &-47 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-47}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{47}{29} & & \\ & V = \left\{ \frac{47}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+4)& = & -12 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+24& = &-12+10+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-2-24 \\\Leftrightarrow & 11x& = &-26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-2)& = & 7 \color{red}{-} (-1+x) \\\Leftrightarrow & -18x-6& = &7+1-x \\\Leftrightarrow & -18x \color{red}{-6} & = &8 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &8+6 \\\Leftrightarrow & -17x& = &14 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{14}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-14}{17} & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+4)& = & 1 \color{red}{+} (-13+x) \\\Leftrightarrow & 20x+16& = &1-13+x \\\Leftrightarrow & 20x \color{red}{+16} & = &-12 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &-12-16 \\\Leftrightarrow & 19x& = &-28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-28}{19} & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x+6)& = & -7 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+36& = &-7+7-x \\\Leftrightarrow & 12x \color{red}{+36} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &0-36 \\\Leftrightarrow & 13x& = &-36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x+5)& = & 12 \color{red}{+} (13+x) \\\Leftrightarrow & 24x+20& = &12+13+x \\\Leftrightarrow & 24x \color{red}{+20} & = &25 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &25-20 \\\Leftrightarrow & 23x& = &5 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{5}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+1)& = & -1 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x+5& = &-1-15+x \\\Leftrightarrow & -30x \color{red}{+5} & = &-16 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -30x-x& = &-16-5 \\\Leftrightarrow & -31x& = &-21 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-21}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{21}{31} & & \\ & V = \left\{ \frac{21}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x+5)& = & 4 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x+10& = &4-14+x \\\Leftrightarrow & -12x \color{red}{+10} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -12x-x& = &-10-10 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)