Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+3)& = & -1 \color{red}{-} (-5+x) \\\Leftrightarrow & -6x+18& = &-1+5-x \\\Leftrightarrow & -6x \color{red}{+18} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &4-18 \\\Leftrightarrow & -5x& = &-14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x-7)& = & 11 \color{red}{-} (6+x) \\\Leftrightarrow & -2x-14& = &11-6-x \\\Leftrightarrow & -2x \color{red}{-14} & = &5 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -2x+x& = &5+14 \\\Leftrightarrow & -x& = &19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{19}{ \color{red}{-1} } \\\Leftrightarrow & x = -19 & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+2)& = & 4 \color{red}{+} (-10-5x) \\\Leftrightarrow & -8x+8& = &4-10-5x \\\Leftrightarrow & -8x \color{red}{+8} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -8x+5x& = &-6-8 \\\Leftrightarrow & -3x& = &-14 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-14}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-1)& = & 2 \color{red}{-} (7+x) \\\Leftrightarrow & 2x-2& = &2-7-x \\\Leftrightarrow & 2x \color{red}{-2} & = &-5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 2x+x& = &-5+2 \\\Leftrightarrow & 3x& = &-3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-3}{ \color{red}{3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-5)& = & -3 \color{red}{+} (-1+3x) \\\Leftrightarrow & 16x-20& = &-3-1+3x \\\Leftrightarrow & 16x \color{red}{-20} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 16x-3x& = &-4+20 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+2)& = & 11 \color{red}{-} (5+3x) \\\Leftrightarrow & 20x+10& = &11-5-3x \\\Leftrightarrow & 20x \color{red}{+10} & = &6 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 20x+3x& = &6-10 \\\Leftrightarrow & 23x& = &-4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x+7)& = & -13 \color{red}{-} (3+3x) \\\Leftrightarrow & -2x+14& = &-13-3-3x \\\Leftrightarrow & -2x \color{red}{+14} & = &-16 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -2x+3x& = &-16-14 \\\Leftrightarrow & x& = &-30 \\ & V = \left\{ -30 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x-7)& = & -2 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x-35& = &-2-6+x \\\Leftrightarrow & 30x \color{red}{-35} & = &-8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 30x-x& = &-8+35 \\\Leftrightarrow & 29x& = &27 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{27}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{27}{29} & & \\ & V = \left\{ \frac{27}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-1)& = & -8 \color{red}{-} (5+x) \\\Leftrightarrow & 12x-2& = &-8-5-x \\\Leftrightarrow & 12x \color{red}{-2} & = &-13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &-13+2 \\\Leftrightarrow & 13x& = &-11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-2)& = & 4 \color{red}{-} (15-4x) \\\Leftrightarrow & -5x-10& = &4-15+4x \\\Leftrightarrow & -5x \color{red}{-10} & = &-11 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-4x} & = &-11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+10} \\\Leftrightarrow & -5x-4x& = &-11+10 \\\Leftrightarrow & -9x& = &-1 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-1}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-4)& = & 15 \color{red}{-} (11+x) \\\Leftrightarrow & 18x-24& = &15-11-x \\\Leftrightarrow & 18x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 18x+x& = &4+24 \\\Leftrightarrow & 19x& = &28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{28}{19} & & \\ & V = \left\{ \frac{28}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x+1)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & -30x+6& = &-9-9-x \\\Leftrightarrow & -30x \color{red}{+6} & = &-18 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -30x+x& = &-18-6 \\\Leftrightarrow & -29x& = &-24 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-24}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)