Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x-3)& = & 15 \color{red}{-} (13+x) \\\Leftrightarrow & 12x-12& = &15-13-x \\\Leftrightarrow & 12x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &2+12 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+5)& = & 14 \color{red}{+} (1+4x) \\\Leftrightarrow & 3x+15& = &14+1+4x \\\Leftrightarrow & 3x \color{red}{+15} & = &15 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 3x-4x& = &15-15 \\\Leftrightarrow & -x& = &0 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{0}{ \color{red}{-1} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x+1)& = & -1 \color{red}{-} (12-2x) \\\Leftrightarrow & -3x+3& = &-1-12+2x \\\Leftrightarrow & -3x \color{red}{+3} & = &-13 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -3x-2x& = &-13-3 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x-1)& = & -8 \color{red}{+} (8+x) \\\Leftrightarrow & 24x-4& = &-8+8+x \\\Leftrightarrow & 24x \color{red}{-4} & = &0 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 24x-x& = &0+4 \\\Leftrightarrow & 23x& = &4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-5)& = & 5 \color{red}{-} (4+x) \\\Leftrightarrow & 4x-10& = &5-4-x \\\Leftrightarrow & 4x \color{red}{-10} & = &1 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 4x+x& = &1+10 \\\Leftrightarrow & 5x& = &11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x+7)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & 6x+21& = &9+7-x \\\Leftrightarrow & 6x \color{red}{+21} & = &16 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 6x+x& = &16-21 \\\Leftrightarrow & 7x& = &-5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x+2)& = & 11 \color{red}{+} (13-3x) \\\Leftrightarrow & -16x+8& = &11+13-3x \\\Leftrightarrow & -16x \color{red}{+8} & = &24 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -16x+3x& = &24-8 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x+4)& = & -8 \color{red}{-} (4-2x) \\\Leftrightarrow & -3x+12& = &-8-4+2x \\\Leftrightarrow & -3x \color{red}{+12} & = &-12 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & -3x-2x& = &-12-12 \\\Leftrightarrow & -5x& = &-24 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-24}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{24}{5} & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x+2)& = & 10 \color{red}{+} (-10+x) \\\Leftrightarrow & -8x+8& = &10-10+x \\\Leftrightarrow & -8x \color{red}{+8} & = &0 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &0-8 \\\Leftrightarrow & -9x& = &-8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-3)& = & 15 \color{red}{+} (-10+3x) \\\Leftrightarrow & 8x-12& = &15-10+3x \\\Leftrightarrow & 8x \color{red}{-12} & = &5 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 8x-3x& = &5+12 \\\Leftrightarrow & 5x& = &17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x+5)& = & 3 \color{red}{+} (-2+x) \\\Leftrightarrow & 8x+10& = &3-2+x \\\Leftrightarrow & 8x \color{red}{+10} & = &1 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 8x-x& = &1-10 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x-6)& = & -13 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x-12& = &-13+14-x \\\Leftrightarrow & 6x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &1+12 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)