Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x-5)& = & 14 \color{red}{+} (11-3x) \\\Leftrightarrow & 25x-25& = &14+11-3x \\\Leftrightarrow & 25x \color{red}{-25} & = &25 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 25x+3x& = &25+25 \\\Leftrightarrow & 28x& = &50 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{50}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{25}{14} & & \\ & V = \left\{ \frac{25}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+4)& = & -14 \color{red}{+} (7+x) \\\Leftrightarrow & 20x+16& = &-14+7+x \\\Leftrightarrow & 20x \color{red}{+16} & = &-7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &-7-16 \\\Leftrightarrow & 19x& = &-23 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-23}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x+1)& = & -2 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x+5& = &-2+2-x \\\Leftrightarrow & -30x \color{red}{+5} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -30x+x& = &0-5 \\\Leftrightarrow & -29x& = &-5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x+6)& = & 5 \color{red}{-} (-15-5x) \\\Leftrightarrow & -6x+18& = &5+15+5x \\\Leftrightarrow & -6x \color{red}{+18} & = &20 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -6x-5x& = &20-18 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x+3)& = & 3 \color{red}{+} (14+x) \\\Leftrightarrow & -25x+15& = &3+14+x \\\Leftrightarrow & -25x \color{red}{+15} & = &17 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -25x-x& = &17-15 \\\Leftrightarrow & -26x& = &2 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{2}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x+1)& = & -15 \color{red}{+} (-14+4x) \\\Leftrightarrow & 9x+3& = &-15-14+4x \\\Leftrightarrow & 9x \color{red}{+3} & = &-29 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{-4x} & = &-29 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-3} \\\Leftrightarrow & 9x-4x& = &-29-3 \\\Leftrightarrow & 5x& = &-32 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-32}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-32}{5} & & \\ & V = \left\{ \frac{-32}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x-7)& = & 6 \color{red}{-} (-5-3x) \\\Leftrightarrow & -4x-14& = &6+5+3x \\\Leftrightarrow & -4x \color{red}{-14} & = &11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -4x-3x& = &11+14 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-2)& = & -15 \color{red}{-} (-2-5x) \\\Leftrightarrow & 6x-4& = &-15+2+5x \\\Leftrightarrow & 6x \color{red}{-4} & = &-13 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 6x-5x& = &-13+4 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+3)& = & -15 \color{red}{+} (-3-5x) \\\Leftrightarrow & -36x+18& = &-15-3-5x \\\Leftrightarrow & -36x \color{red}{+18} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -36x+5x& = &-18-18 \\\Leftrightarrow & -31x& = &-36 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-36}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{36}{31} & & \\ & V = \left\{ \frac{36}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x-7)& = & 2 \color{red}{+} (11+x) \\\Leftrightarrow & -20x-35& = &2+11+x \\\Leftrightarrow & -20x \color{red}{-35} & = &13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -20x-x& = &13+35 \\\Leftrightarrow & -21x& = &48 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{48}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+7)& = & -13 \color{red}{+} (-11-5x) \\\Leftrightarrow & 36x+42& = &-13-11-5x \\\Leftrightarrow & 36x \color{red}{+42} & = &-24 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-24 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 36x+5x& = &-24-42 \\\Leftrightarrow & 41x& = &-66 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-66}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-66}{41} & & \\ & V = \left\{ \frac{-66}{41} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+2)& = & 14 \color{red}{-} (5+x) \\\Leftrightarrow & 6x+4& = &14-5-x \\\Leftrightarrow & 6x \color{red}{+4} & = &9 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 6x+x& = &9-4 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)