Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-5)& = & 2 \color{red}{-} (-2-3x) \\\Leftrightarrow & 4x-10& = &2+2+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &4 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &4+10 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+7)& = & -6 \color{red}{+} (-12+x) \\\Leftrightarrow & 2x+14& = &-6-12+x \\\Leftrightarrow & 2x \color{red}{+14} & = &-18 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 2x-x& = &-18-14 \\\Leftrightarrow & x& = &-32 \\ & V = \left\{ -32 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+3)& = & -9 \color{red}{+} (1+x) \\\Leftrightarrow & -8x+12& = &-9+1+x \\\Leftrightarrow & -8x \color{red}{+12} & = &-8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -8x-x& = &-8-12 \\\Leftrightarrow & -9x& = &-20 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-20}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{20}{9} & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+2)& = & -11 \color{red}{-} (12+x) \\\Leftrightarrow & -24x+8& = &-11-12-x \\\Leftrightarrow & -24x \color{red}{+8} & = &-23 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -24x+x& = &-23-8 \\\Leftrightarrow & -23x& = &-31 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-31}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{31}{23} & & \\ & V = \left\{ \frac{31}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x+4)& = & 6 \color{red}{+} (7+3x) \\\Leftrightarrow & -4x+16& = &6+7+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &13 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &13-16 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+7)& = & -11 \color{red}{+} (-13+x) \\\Leftrightarrow & 30x+42& = &-11-13+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-24 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-24-42 \\\Leftrightarrow & 29x& = &-66 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-66}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-66}{29} & & \\ & V = \left\{ \frac{-66}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-5)& = & -3 \color{red}{-} (1+x) \\\Leftrightarrow & -3x-15& = &-3-1-x \\\Leftrightarrow & -3x \color{red}{-15} & = &-4 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -3x+x& = &-4+15 \\\Leftrightarrow & -2x& = &11 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{11}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-11}{2} & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-4)& = & 7 \color{red}{-} (10+x) \\\Leftrightarrow & -20x-16& = &7-10-x \\\Leftrightarrow & -20x \color{red}{-16} & = &-3 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &-3+16 \\\Leftrightarrow & -19x& = &13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (6x-7)& = & -10 \color{red}{+} (-15+x) \\\Leftrightarrow & 12x-14& = &-10-15+x \\\Leftrightarrow & 12x \color{red}{-14} & = &-25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &-25+14 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x-2)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & -18x-6& = &-11-10+x \\\Leftrightarrow & -18x \color{red}{-6} & = &-21 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -18x-x& = &-21+6 \\\Leftrightarrow & -19x& = &-15 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-15}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{15}{19} & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x+3)& = & 8 \color{red}{+} (14+x) \\\Leftrightarrow & 24x+18& = &8+14+x \\\Leftrightarrow & 24x \color{red}{+18} & = &22 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 24x-x& = &22-18 \\\Leftrightarrow & 23x& = &4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-7)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x-42& = &13+1-x \\\Leftrightarrow & 12x \color{red}{-42} & = &14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 12x+x& = &14+42 \\\Leftrightarrow & 13x& = &56 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{56}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{56}{13} & & \\ & V = \left\{ \frac{56}{13} \right\} & \\\end{align}\)