Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x-4)& = & -2 \color{red}{-} (4+x) \\\Leftrightarrow & 4x-16& = &-2-4-x \\\Leftrightarrow & 4x \color{red}{-16} & = &-6 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 4x+x& = &-6+16 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+2)& = & 13 \color{red}{-} (4+x) \\\Leftrightarrow & -24x+12& = &13-4-x \\\Leftrightarrow & -24x \color{red}{+12} & = &9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &9-12 \\\Leftrightarrow & -23x& = &-3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x+7)& = & 11 \color{red}{-} (15-5x) \\\Leftrightarrow & 6x+21& = &11-15+5x \\\Leftrightarrow & 6x \color{red}{+21} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 6x-5x& = &-4-21 \\\Leftrightarrow & x& = &-25 \\ & V = \left\{ -25 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-2)& = & -7 \color{red}{-} (2+x) \\\Leftrightarrow & 2x-4& = &-7-2-x \\\Leftrightarrow & 2x \color{red}{-4} & = &-9 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 2x+x& = &-9+4 \\\Leftrightarrow & 3x& = &-5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x+4)& = & -1 \color{red}{-} (13+4x) \\\Leftrightarrow & -9x+12& = &-1-13-4x \\\Leftrightarrow & -9x \color{red}{+12} & = &-14 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+4x} & = &-14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-12} \\\Leftrightarrow & -9x+4x& = &-14-12 \\\Leftrightarrow & -5x& = &-26 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-26}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{26}{5} & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x-4)& = & 1 \color{red}{-} (10+x) \\\Leftrightarrow & -8x-8& = &1-10-x \\\Leftrightarrow & -8x \color{red}{-8} & = &-9 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &-9+8 \\\Leftrightarrow & -7x& = &-1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-3)& = & 10 \color{red}{-} (13+x) \\\Leftrightarrow & 20x-15& = &10-13-x \\\Leftrightarrow & 20x \color{red}{-15} & = &-3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 20x+x& = &-3+15 \\\Leftrightarrow & 21x& = &12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x+6)& = & 12 \color{red}{+} (-7-5x) \\\Leftrightarrow & -8x+24& = &12-7-5x \\\Leftrightarrow & -8x \color{red}{+24} & = &5 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -8x+5x& = &5-24 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x+6)& = & 15 \color{red}{-} (7+x) \\\Leftrightarrow & 8x+12& = &15-7-x \\\Leftrightarrow & 8x \color{red}{+12} & = &8 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 8x+x& = &8-12 \\\Leftrightarrow & 9x& = &-4 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-4}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x-1)& = & 11 \color{red}{-} (8+x) \\\Leftrightarrow & -24x-6& = &11-8-x \\\Leftrightarrow & -24x \color{red}{-6} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -24x+x& = &3+6 \\\Leftrightarrow & -23x& = &9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x+7)& = & 9 \color{red}{+} (14-4x) \\\Leftrightarrow & -5x+35& = &9+14-4x \\\Leftrightarrow & -5x \color{red}{+35} & = &23 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &23 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -5x+4x& = &23-35 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x+6)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & 12x+24& = &-11-15-x \\\Leftrightarrow & 12x \color{red}{+24} & = &-26 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &-26-24 \\\Leftrightarrow & 13x& = &-50 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-50}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-50}{13} & & \\ & V = \left\{ \frac{-50}{13} \right\} & \\\end{align}\)