Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+2)& = & -7 \color{red}{-} (-3-2x) \\\Leftrightarrow & 15x+6& = &-7+3+2x \\\Leftrightarrow & 15x \color{red}{+6} & = &-4 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & 15x-2x& = &-4-6 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-1)& = & 7 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-3& = &7-6+x \\\Leftrightarrow & 6x \color{red}{-3} & = &1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 6x-x& = &1+3 \\\Leftrightarrow & 5x& = &4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-x+4)& = & -3 \color{red}{+} (-5+4x) \\\Leftrightarrow & -3x+12& = &-3-5+4x \\\Leftrightarrow & -3x \color{red}{+12} & = &-8 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & -3x-4x& = &-8-12 \\\Leftrightarrow & -7x& = &-20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x+6)& = & 2 \color{red}{-} (3-3x) \\\Leftrightarrow & -4x+24& = &2-3+3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -4x-3x& = &-1-24 \\\Leftrightarrow & -7x& = &-25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+6)& = & 11 \color{red}{+} (-10-5x) \\\Leftrightarrow & 6x+36& = &11-10-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &1-36 \\\Leftrightarrow & 11x& = &-35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x+2)& = & -15 \color{red}{-} (-3+x) \\\Leftrightarrow & 36x+12& = &-15+3-x \\\Leftrightarrow & 36x \color{red}{+12} & = &-12 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 36x+x& = &-12-12 \\\Leftrightarrow & 37x& = &-24 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-24}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-24}{37} & & \\ & V = \left\{ \frac{-24}{37} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x-5)& = & -4 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-15& = &-4+10+x \\\Leftrightarrow & 12x \color{red}{-15} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &6+15 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-3)& = & -10 \color{red}{-} (15-3x) \\\Leftrightarrow & -10x-6& = &-10-15+3x \\\Leftrightarrow & -10x \color{red}{-6} & = &-25 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -10x-3x& = &-25+6 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-1)& = & -7 \color{red}{-} (-3+x) \\\Leftrightarrow & -18x-3& = &-7+3-x \\\Leftrightarrow & -18x \color{red}{-3} & = &-4 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -18x+x& = &-4+3 \\\Leftrightarrow & -17x& = &-1 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-1}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{1}{17} & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x+1)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 18x+3& = &-10-3-x \\\Leftrightarrow & 18x \color{red}{+3} & = &-13 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 18x+x& = &-13-3 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x-4)& = & -5 \color{red}{+} (-12-5x) \\\Leftrightarrow & 8x-16& = &-5-12-5x \\\Leftrightarrow & 8x \color{red}{-16} & = &-17 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+16} \\\Leftrightarrow & 8x+5x& = &-17+16 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x-1)& = & -1 \color{red}{-} (-15+x) \\\Leftrightarrow & 24x-4& = &-1+15-x \\\Leftrightarrow & 24x \color{red}{-4} & = &14 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &14+4 \\\Leftrightarrow & 25x& = &18 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{18}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{18}{25} & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)