Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+6)& = & 4 \color{red}{+} (3+3x) \\\Leftrightarrow & 8x+12& = &4+3+3x \\\Leftrightarrow & 8x \color{red}{+12} & = &7 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 8x-3x& = &7-12 \\\Leftrightarrow & 5x& = &-5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-5}{ \color{red}{5} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x-5)& = & -15 \color{red}{+} (-9-4x) \\\Leftrightarrow & -25x-25& = &-15-9-4x \\\Leftrightarrow & -25x \color{red}{-25} & = &-24 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-24 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -25x+4x& = &-24+25 \\\Leftrightarrow & -21x& = &1 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{1}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x-3)& = & -11 \color{red}{-} (-15+x) \\\Leftrightarrow & 6x-18& = &-11+15-x \\\Leftrightarrow & 6x \color{red}{-18} & = &4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 6x+x& = &4+18 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-2)& = & -7 \color{red}{-} (11+x) \\\Leftrightarrow & 30x-10& = &-7-11-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-18 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-18+10 \\\Leftrightarrow & 31x& = &-8 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-8}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-8}{31} & & \\ & V = \left\{ \frac{-8}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-4)& = & 2 \color{red}{-} (1+x) \\\Leftrightarrow & 12x-24& = &2-1-x \\\Leftrightarrow & 12x \color{red}{-24} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &1+24 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+6)& = & 9 \color{red}{+} (-8+x) \\\Leftrightarrow & 8x+24& = &9-8+x \\\Leftrightarrow & 8x \color{red}{+24} & = &1 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 8x-x& = &1-24 \\\Leftrightarrow & 7x& = &-23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-6)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-12& = &-11-11-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-22 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-22+12 \\\Leftrightarrow & 13x& = &-10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+6)& = & 7 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+18& = &7-8+x \\\Leftrightarrow & -12x \color{red}{+18} & = &-1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &-1-18 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x+2)& = & -8 \color{red}{-} (-2-5x) \\\Leftrightarrow & 18x+6& = &-8+2+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &-6-6 \\\Leftrightarrow & 13x& = &-12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x-6)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & 9x-18& = &-8-14+x \\\Leftrightarrow & 9x \color{red}{-18} & = &-22 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 9x-x& = &-22+18 \\\Leftrightarrow & 8x& = &-4 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-4}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+3)& = & 15 \color{red}{+} (-13-5x) \\\Leftrightarrow & 36x+18& = &15-13-5x \\\Leftrightarrow & 36x \color{red}{+18} & = &2 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 36x+5x& = &2-18 \\\Leftrightarrow & 41x& = &-16 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-16}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-16}{41} & & \\ & V = \left\{ \frac{-16}{41} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x+5)& = & -15 \color{red}{-} (-5-5x) \\\Leftrightarrow & 36x+30& = &-15+5+5x \\\Leftrightarrow & 36x \color{red}{+30} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & 36x-5x& = &-10-30 \\\Leftrightarrow & 31x& = &-40 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-40}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-40}{31} & & \\ & V = \left\{ \frac{-40}{31} \right\} & \\\end{align}\)