Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-7)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & -6x-21& = &11-10-x \\\Leftrightarrow & -6x \color{red}{-21} & = &1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -6x+x& = &1+21 \\\Leftrightarrow & -5x& = &22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+4)& = & 12 \color{red}{+} (-2+x) \\\Leftrightarrow & 30x+20& = &12-2+x \\\Leftrightarrow & 30x \color{red}{+20} & = &10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &10-20 \\\Leftrightarrow & 29x& = &-10 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-10}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-10}{29} & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-4x+7)& = & 4 \color{red}{+} (11+x) \\\Leftrightarrow & -8x+14& = &4+11+x \\\Leftrightarrow & -8x \color{red}{+14} & = &15 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -8x-x& = &15-14 \\\Leftrightarrow & -9x& = &1 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{1}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-1}{9} & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-5x+4)& = & -1 \color{red}{+} (-3-3x) \\\Leftrightarrow & -10x+8& = &-1-3-3x \\\Leftrightarrow & -10x \color{red}{+8} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -10x+3x& = &-4-8 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-6)& = & 12 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-18& = &12-2+x \\\Leftrightarrow & -12x \color{red}{-18} & = &10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &10+18 \\\Leftrightarrow & -13x& = &28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+2)& = & -12 \color{red}{+} (-4+4x) \\\Leftrightarrow & -3x+6& = &-12-4+4x \\\Leftrightarrow & -3x \color{red}{+6} & = &-16 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &-16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & -3x-4x& = &-16-6 \\\Leftrightarrow & -7x& = &-22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x+6)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & 2x+12& = &-5-15+x \\\Leftrightarrow & 2x \color{red}{+12} & = &-20 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 2x-x& = &-20-12 \\\Leftrightarrow & x& = &-32 \\ & V = \left\{ -32 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x+6)& = & 14 \color{red}{+} (7-4x) \\\Leftrightarrow & -25x+30& = &14+7-4x \\\Leftrightarrow & -25x \color{red}{+30} & = &21 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & -25x+4x& = &21-30 \\\Leftrightarrow & -21x& = &-9 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-9}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x+4)& = & 9 \color{red}{+} (7+x) \\\Leftrightarrow & 20x+20& = &9+7+x \\\Leftrightarrow & 20x \color{red}{+20} & = &16 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &16-20 \\\Leftrightarrow & 19x& = &-4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-5)& = & 3 \color{red}{+} (-6+x) \\\Leftrightarrow & -24x-30& = &3-6+x \\\Leftrightarrow & -24x \color{red}{-30} & = &-3 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -24x-x& = &-3+30 \\\Leftrightarrow & -25x& = &27 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{27}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-27}{25} & & \\ & V = \left\{ \frac{-27}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x-7)& = & -4 \color{red}{+} (8+x) \\\Leftrightarrow & -6x-14& = &-4+8+x \\\Leftrightarrow & -6x \color{red}{-14} & = &4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -6x-x& = &4+14 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x+3)& = & -6 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+12& = &-6-4+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-10-12 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)