Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x+3)& = & -3 \color{red}{-} (-5+x) \\\Leftrightarrow & -8x+12& = &-3+5-x \\\Leftrightarrow & -8x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &2-12 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-7)& = & 9 \color{red}{+} (11+x) \\\Leftrightarrow & 8x-28& = &9+11+x \\\Leftrightarrow & 8x \color{red}{-28} & = &20 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 8x-x& = &20+28 \\\Leftrightarrow & 7x& = &48 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{48}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{48}{7} & & \\ & V = \left\{ \frac{48}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+5)& = & 5 \color{red}{-} (-13-3x) \\\Leftrightarrow & -4x+20& = &5+13+3x \\\Leftrightarrow & -4x \color{red}{+20} & = &18 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -4x-3x& = &18-20 \\\Leftrightarrow & -7x& = &-2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+4)& = & 5 \color{red}{-} (15+x) \\\Leftrightarrow & 20x+16& = &5-15-x \\\Leftrightarrow & 20x \color{red}{+16} & = &-10 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 20x+x& = &-10-16 \\\Leftrightarrow & 21x& = &-26 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-26}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-26}{21} & & \\ & V = \left\{ \frac{-26}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+4)& = & 15 \color{red}{-} (2+x) \\\Leftrightarrow & -24x+16& = &15-2-x \\\Leftrightarrow & -24x \color{red}{+16} & = &13 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &13-16 \\\Leftrightarrow & -23x& = &-3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-5)& = & 1 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-15& = &1-7-x \\\Leftrightarrow & -12x \color{red}{-15} & = &-6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -12x+x& = &-6+15 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x-4)& = & -5 \color{red}{-} (-6-3x) \\\Leftrightarrow & -10x-20& = &-5+6+3x \\\Leftrightarrow & -10x \color{red}{-20} & = &1 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -10x-3x& = &1+20 \\\Leftrightarrow & -13x& = &21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+6)& = & 9 \color{red}{+} (-5+x) \\\Leftrightarrow & -16x+24& = &9-5+x \\\Leftrightarrow & -16x \color{red}{+24} & = &4 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -16x-x& = &4-24 \\\Leftrightarrow & -17x& = &-20 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-20}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{20}{17} & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x+6)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & 2x+12& = &6+10+x \\\Leftrightarrow & 2x \color{red}{+12} & = &16 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 2x-x& = &16-12 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-4)& = & 6 \color{red}{+} (-3+x) \\\Leftrightarrow & -9x-12& = &6-3+x \\\Leftrightarrow & -9x \color{red}{-12} & = &3 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -9x-x& = &3+12 \\\Leftrightarrow & -10x& = &15 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{15}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x-1)& = & -4 \color{red}{-} (-5+x) \\\Leftrightarrow & -10x-2& = &-4+5-x \\\Leftrightarrow & -10x \color{red}{-2} & = &1 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -10x+x& = &1+2 \\\Leftrightarrow & -9x& = &3 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{3}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+4)& = & -2 \color{red}{+} (-13-5x) \\\Leftrightarrow & 6x+12& = &-2-13-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &-15-12 \\\Leftrightarrow & 11x& = &-27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-27}{11} & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)