Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x+2)& = & 5 \color{red}{+} (7+x) \\\Leftrightarrow & 12x+6& = &5+7+x \\\Leftrightarrow & 12x \color{red}{+6} & = &12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &12-6 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x-1)& = & -5 \color{red}{+} (-5+3x) \\\Leftrightarrow & -20x-4& = &-5-5+3x \\\Leftrightarrow & -20x \color{red}{-4} & = &-10 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -20x-3x& = &-10+4 \\\Leftrightarrow & -23x& = &-6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+6)& = & -9 \color{red}{-} (15-4x) \\\Leftrightarrow & -9x+18& = &-9-15+4x \\\Leftrightarrow & -9x \color{red}{+18} & = &-24 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &-24 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & -9x-4x& = &-24-18 \\\Leftrightarrow & -13x& = &-42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{42}{13} & & \\ & V = \left\{ \frac{42}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (x-4)& = & -6 \color{red}{+} (-5+x) \\\Leftrightarrow & 5x-20& = &-6-5+x \\\Leftrightarrow & 5x \color{red}{-20} & = &-11 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 5x-x& = &-11+20 \\\Leftrightarrow & 4x& = &9 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{9}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{9}{4} & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+4)& = & -13 \color{red}{-} (-14+x) \\\Leftrightarrow & -8x+16& = &-13+14-x \\\Leftrightarrow & -8x \color{red}{+16} & = &1 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -8x+x& = &1-16 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+4)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & 12x+16& = &8+11+x \\\Leftrightarrow & 12x \color{red}{+16} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 12x-x& = &19-16 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x+1)& = & 3 \color{red}{+} (7-5x) \\\Leftrightarrow & 18x+3& = &3+7-5x \\\Leftrightarrow & 18x \color{red}{+3} & = &10 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 18x+5x& = &10-3 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x+6)& = & 7 \color{red}{-} (-5-5x) \\\Leftrightarrow & 8x+24& = &7+5+5x \\\Leftrightarrow & 8x \color{red}{+24} & = &12 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 8x-5x& = &12-24 \\\Leftrightarrow & 3x& = &-12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-12}{ \color{red}{3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-4)& = & 11 \color{red}{+} (10-4x) \\\Leftrightarrow & -9x-12& = &11+10-4x \\\Leftrightarrow & -9x \color{red}{-12} & = &21 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & -9x+4x& = &21+12 \\\Leftrightarrow & -5x& = &33 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{33}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-33}{5} & & \\ & V = \left\{ \frac{-33}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+3)& = & -10 \color{red}{-} (4+x) \\\Leftrightarrow & -30x+15& = &-10-4-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-14-15 \\\Leftrightarrow & -29x& = &-29 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-29}{ \color{red}{-29} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-6)& = & -6 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-36& = &-6-10-x \\\Leftrightarrow & 30x \color{red}{-36} & = &-16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &-16+36 \\\Leftrightarrow & 31x& = &20 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{20}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{20}{31} & & \\ & V = \left\{ \frac{20}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-5)& = & -4 \color{red}{+} (6+x) \\\Leftrightarrow & 24x-30& = &-4+6+x \\\Leftrightarrow & 24x \color{red}{-30} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 24x-x& = &2+30 \\\Leftrightarrow & 23x& = &32 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{32}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)