Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x-3)& = & -14 \color{red}{+} (-13+x) \\\Leftrightarrow & -20x-12& = &-14-13+x \\\Leftrightarrow & -20x \color{red}{-12} & = &-27 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -20x-x& = &-27+12 \\\Leftrightarrow & -21x& = &-15 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-15}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x-6)& = & 5 \color{red}{+} (-11+x) \\\Leftrightarrow & 6x-12& = &5-11+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-6+12 \\\Leftrightarrow & 5x& = &6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-2)& = & 7 \color{red}{+} (-2+x) \\\Leftrightarrow & -24x-8& = &7-2+x \\\Leftrightarrow & -24x \color{red}{-8} & = &5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &5+8 \\\Leftrightarrow & -25x& = &13 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{13}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-13}{25} & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-1)& = & -8 \color{red}{+} (-2-5x) \\\Leftrightarrow & 8x-2& = &-8-2-5x \\\Leftrightarrow & 8x \color{red}{-2} & = &-10 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+2} \\\Leftrightarrow & 8x+5x& = &-10+2 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-6)& = & 4 \color{red}{+} (3-2x) \\\Leftrightarrow & -5x-30& = &4+3-2x \\\Leftrightarrow & -5x \color{red}{-30} & = &7 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & -5x+2x& = &7+30 \\\Leftrightarrow & -3x& = &37 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{37}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-37}{3} & & \\ & V = \left\{ \frac{-37}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-4)& = & 15 \color{red}{+} (11+3x) \\\Leftrightarrow & -20x-20& = &15+11+3x \\\Leftrightarrow & -20x \color{red}{-20} & = &26 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &26 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -20x-3x& = &26+20 \\\Leftrightarrow & -23x& = &46 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{46}{ \color{red}{-23} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-1)& = & -7 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-2& = &-7-6+x \\\Leftrightarrow & 12x \color{red}{-2} & = &-13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &-13+2 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-1)& = & -15 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-3& = &-15+7-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-8+3 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+3)& = & 7 \color{red}{-} (5+x) \\\Leftrightarrow & -12x+9& = &7-5-x \\\Leftrightarrow & -12x \color{red}{+9} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &2-9 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x+7)& = & -7 \color{red}{-} (-14+3x) \\\Leftrightarrow & 10x+14& = &-7+14-3x \\\Leftrightarrow & 10x \color{red}{+14} & = &7 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 10x+3x& = &7-14 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+6)& = & 14 \color{red}{-} (13+x) \\\Leftrightarrow & 4x+24& = &14-13-x \\\Leftrightarrow & 4x \color{red}{+24} & = &1 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 4x+x& = &1-24 \\\Leftrightarrow & 5x& = &-23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-6)& = & -7 \color{red}{+} (-10-3x) \\\Leftrightarrow & -4x-12& = &-7-10-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &-17+12 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)