Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-5)& = & 14 \color{red}{-} (7+x) \\\Leftrightarrow & 24x-30& = &14-7-x \\\Leftrightarrow & 24x \color{red}{-30} & = &7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &7+30 \\\Leftrightarrow & 25x& = &37 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{37}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{37}{25} & & \\ & V = \left\{ \frac{37}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x+3)& = & 9 \color{red}{-} (-4+x) \\\Leftrightarrow & -24x+12& = &9+4-x \\\Leftrightarrow & -24x \color{red}{+12} & = &13 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &13-12 \\\Leftrightarrow & -23x& = &1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+2)& = & -8 \color{red}{-} (4+3x) \\\Leftrightarrow & -10x+4& = &-8-4-3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-12 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -10x+3x& = &-12-4 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+7)& = & -4 \color{red}{+} (5+3x) \\\Leftrightarrow & 4x+14& = &-4+5+3x \\\Leftrightarrow & 4x \color{red}{+14} & = &1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & 4x-3x& = &1-14 \\\Leftrightarrow & x& = &-13 \\ & V = \left\{ -13 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-2)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & 20x-10& = &-11-11-x \\\Leftrightarrow & 20x \color{red}{-10} & = &-22 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 20x+x& = &-22+10 \\\Leftrightarrow & 21x& = &-12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x+7)& = & 9 \color{red}{+} (-8+x) \\\Leftrightarrow & -20x+35& = &9-8+x \\\Leftrightarrow & -20x \color{red}{+35} & = &1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -20x-x& = &1-35 \\\Leftrightarrow & -21x& = &-34 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-34}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{34}{21} & & \\ & V = \left\{ \frac{34}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-5)& = & -10 \color{red}{+} (12-3x) \\\Leftrightarrow & 10x-10& = &-10+12-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &2+10 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x-6)& = & 5 \color{red}{-} (3-5x) \\\Leftrightarrow & -18x-18& = &5-3+5x \\\Leftrightarrow & -18x \color{red}{-18} & = &2 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -18x-5x& = &2+18 \\\Leftrightarrow & -23x& = &20 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{20}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-20}{23} & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (6x+4)& = & -3 \color{red}{+} (-2+x) \\\Leftrightarrow & 30x+20& = &-3-2+x \\\Leftrightarrow & 30x \color{red}{+20} & = &-5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &-5-20 \\\Leftrightarrow & 29x& = &-25 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-25}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-25}{29} & & \\ & V = \left\{ \frac{-25}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x+5)& = & 8 \color{red}{+} (8+x) \\\Leftrightarrow & -3x+15& = &8+8+x \\\Leftrightarrow & -3x \color{red}{+15} & = &16 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -3x-x& = &16-15 \\\Leftrightarrow & -4x& = &1 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{1}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+7)& = & -4 \color{red}{+} (9-5x) \\\Leftrightarrow & 6x+21& = &-4+9-5x \\\Leftrightarrow & 6x \color{red}{+21} & = &5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & 6x+5x& = &5-21 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+2)& = & -3 \color{red}{-} (12+x) \\\Leftrightarrow & -16x+8& = &-3-12-x \\\Leftrightarrow & -16x \color{red}{+8} & = &-15 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -16x+x& = &-15-8 \\\Leftrightarrow & -15x& = &-23 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-23}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{23}{15} & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)