Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-2)& = & 5 \color{red}{-} (-8-5x) \\\Leftrightarrow & 6x-4& = &5+8+5x \\\Leftrightarrow & 6x \color{red}{-4} & = &13 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 6x-5x& = &13+4 \\\Leftrightarrow & x& = &17 \\ & V = \left\{ 17 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x+5)& = & 10 \color{red}{-} (13+x) \\\Leftrightarrow & -2x+10& = &10-13-x \\\Leftrightarrow & -2x \color{red}{+10} & = &-3 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -2x+x& = &-3-10 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x-4)& = & -12 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x-16& = &-12-8+x \\\Leftrightarrow & -12x \color{red}{-16} & = &-20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -12x-x& = &-20+16 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x-3)& = & 15 \color{red}{+} (-2+x) \\\Leftrightarrow & -4x-12& = &15-2+x \\\Leftrightarrow & -4x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -4x-x& = &13+12 \\\Leftrightarrow & -5x& = &25 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{25}{ \color{red}{-5} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-7)& = & 5 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x-28& = &5+8+3x \\\Leftrightarrow & 4x \color{red}{-28} & = &13 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & 4x-3x& = &13+28 \\\Leftrightarrow & x& = &41 \\ & V = \left\{ 41 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+1)& = & -10 \color{red}{-} (1+x) \\\Leftrightarrow & -30x+5& = &-10-1-x \\\Leftrightarrow & -30x \color{red}{+5} & = &-11 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -30x+x& = &-11-5 \\\Leftrightarrow & -29x& = &-16 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-16}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{16}{29} & & \\ & V = \left\{ \frac{16}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+3)& = & 10 \color{red}{+} (3+x) \\\Leftrightarrow & 12x+9& = &10+3+x \\\Leftrightarrow & 12x \color{red}{+9} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 12x-x& = &13-9 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+3)& = & -14 \color{red}{+} (10+x) \\\Leftrightarrow & 6x+18& = &-14+10+x \\\Leftrightarrow & 6x \color{red}{+18} & = &-4 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 6x-x& = &-4-18 \\\Leftrightarrow & 5x& = &-22 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-22}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x-3)& = & -11 \color{red}{-} (11-3x) \\\Leftrightarrow & 10x-6& = &-11-11+3x \\\Leftrightarrow & 10x \color{red}{-6} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 10x-3x& = &-22+6 \\\Leftrightarrow & 7x& = &-16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-5)& = & -5 \color{red}{-} (-4-3x) \\\Leftrightarrow & 10x-25& = &-5+4+3x \\\Leftrightarrow & 10x \color{red}{-25} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & 10x-3x& = &-1+25 \\\Leftrightarrow & 7x& = &24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-4x+6)& = & 7 \color{red}{+} (-12+3x) \\\Leftrightarrow & -16x+24& = &7-12+3x \\\Leftrightarrow & -16x \color{red}{+24} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -16x-3x& = &-5-24 \\\Leftrightarrow & -19x& = &-29 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-29}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{29}{19} & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-5)& = & -2 \color{red}{+} (8+x) \\\Leftrightarrow & 8x-10& = &-2+8+x \\\Leftrightarrow & 8x \color{red}{-10} & = &6 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 8x-x& = &6+10 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)