Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x+1)& = & -5 \color{red}{-} (12-5x) \\\Leftrightarrow & 6x+2& = &-5-12+5x \\\Leftrightarrow & 6x \color{red}{+2} & = &-17 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 6x-5x& = &-17-2 \\\Leftrightarrow & x& = &-19 \\ & V = \left\{ -19 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+3)& = & -7 \color{red}{-} (8-5x) \\\Leftrightarrow & -6x+9& = &-7-8+5x \\\Leftrightarrow & -6x \color{red}{+9} & = &-15 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & -6x-5x& = &-15-9 \\\Leftrightarrow & -11x& = &-24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-6)& = & -3 \color{red}{+} (7-3x) \\\Leftrightarrow & -4x-24& = &-3+7-3x \\\Leftrightarrow & -4x \color{red}{-24} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -4x+3x& = &4+24 \\\Leftrightarrow & -x& = &28 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{28}{ \color{red}{-1} } \\\Leftrightarrow & x = -28 & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x-4)& = & 2 \color{red}{+} (-8+3x) \\\Leftrightarrow & -10x-8& = &2-8+3x \\\Leftrightarrow & -10x \color{red}{-8} & = &-6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -10x-3x& = &-6+8 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+5)& = & -14 \color{red}{-} (-9-4x) \\\Leftrightarrow & -5x+25& = &-14+9+4x \\\Leftrightarrow & -5x \color{red}{+25} & = &-5 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & -5x-4x& = &-5-25 \\\Leftrightarrow & -9x& = &-30 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-30}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-6)& = & 11 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x-12& = &11-5+x \\\Leftrightarrow & -12x \color{red}{-12} & = &6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &6+12 \\\Leftrightarrow & -13x& = &18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+6)& = & 14 \color{red}{+} (7+x) \\\Leftrightarrow & -20x+30& = &14+7+x \\\Leftrightarrow & -20x \color{red}{+30} & = &21 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -20x-x& = &21-30 \\\Leftrightarrow & -21x& = &-9 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-9}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x-1)& = & -7 \color{red}{+} (13-5x) \\\Leftrightarrow & -18x-3& = &-7+13-5x \\\Leftrightarrow & -18x \color{red}{-3} & = &6 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -18x+5x& = &6+3 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+4)& = & 1 \color{red}{-} (13+2x) \\\Leftrightarrow & 25x+20& = &1-13-2x \\\Leftrightarrow & 25x \color{red}{+20} & = &-12 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &-12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 25x+2x& = &-12-20 \\\Leftrightarrow & 27x& = &-32 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{-32}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{-32}{27} & & \\ & V = \left\{ \frac{-32}{27} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x+5)& = & -13 \color{red}{-} (-8-3x) \\\Leftrightarrow & -4x+20& = &-13+8+3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -4x-3x& = &-5-20 \\\Leftrightarrow & -7x& = &-25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-4)& = & 3 \color{red}{-} (-6+x) \\\Leftrightarrow & -20x-16& = &3+6-x \\\Leftrightarrow & -20x \color{red}{-16} & = &9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &9+16 \\\Leftrightarrow & -19x& = &25 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{25}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-25}{19} & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x+2)& = & -4 \color{red}{+} (-1-5x) \\\Leftrightarrow & 16x+8& = &-4-1-5x \\\Leftrightarrow & 16x \color{red}{+8} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & 16x+5x& = &-5-8 \\\Leftrightarrow & 21x& = &-13 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-13}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)