Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x+4)& = & -14 \color{red}{+} (10+x) \\\Leftrightarrow & 36x+24& = &-14+10+x \\\Leftrightarrow & 36x \color{red}{+24} & = &-4 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 36x-x& = &-4-24 \\\Leftrightarrow & 35x& = &-28 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-28}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x-6)& = & -11 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x-30& = &-11-14+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-25 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-25+30 \\\Leftrightarrow & 29x& = &5 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{5}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x-1)& = & 8 \color{red}{-} (-4+x) \\\Leftrightarrow & 10x-2& = &8+4-x \\\Leftrightarrow & 10x \color{red}{-2} & = &12 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 10x+x& = &12+2 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x-7)& = & 12 \color{red}{-} (-8+4x) \\\Leftrightarrow & 15x-21& = &12+8-4x \\\Leftrightarrow & 15x \color{red}{-21} & = &20 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &20 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 15x+4x& = &20+21 \\\Leftrightarrow & 19x& = &41 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{41}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{41}{19} & & \\ & V = \left\{ \frac{41}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x+7)& = & -12 \color{red}{+} (6+x) \\\Leftrightarrow & -20x+35& = &-12+6+x \\\Leftrightarrow & -20x \color{red}{+35} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -20x-x& = &-6-35 \\\Leftrightarrow & -21x& = &-41 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-41}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{41}{21} & & \\ & V = \left\{ \frac{41}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-3)& = & 10 \color{red}{+} (11-3x) \\\Leftrightarrow & 10x-15& = &10+11-3x \\\Leftrightarrow & 10x \color{red}{-15} & = &21 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 10x+3x& = &21+15 \\\Leftrightarrow & 13x& = &36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{36}{13} & & \\ & V = \left\{ \frac{36}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-7)& = & 9 \color{red}{+} (-11+2x) \\\Leftrightarrow & -15x-35& = &9-11+2x \\\Leftrightarrow & -15x \color{red}{-35} & = &-2 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -15x-2x& = &-2+35 \\\Leftrightarrow & -17x& = &33 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{33}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-33}{17} & & \\ & V = \left\{ \frac{-33}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-1)& = & 4 \color{red}{-} (-10+x) \\\Leftrightarrow & 2x-2& = &4+10-x \\\Leftrightarrow & 2x \color{red}{-2} & = &14 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 2x+x& = &14+2 \\\Leftrightarrow & 3x& = &16 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{16}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{16}{3} & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x-4)& = & 10 \color{red}{+} (9+x) \\\Leftrightarrow & 8x-16& = &10+9+x \\\Leftrightarrow & 8x \color{red}{-16} & = &19 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 8x-x& = &19+16 \\\Leftrightarrow & 7x& = &35 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{35}{ \color{red}{7} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x-5)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & 8x-10& = &3-5-x \\\Leftrightarrow & 8x \color{red}{-10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 8x+x& = &-2+10 \\\Leftrightarrow & 9x& = &8 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{8}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-3)& = & 8 \color{red}{-} (1-5x) \\\Leftrightarrow & -8x-6& = &8-1+5x \\\Leftrightarrow & -8x \color{red}{-6} & = &7 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -8x-5x& = &7+6 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x-6)& = & 1 \color{red}{+} (-13+3x) \\\Leftrightarrow & 10x-30& = &1-13+3x \\\Leftrightarrow & 10x \color{red}{-30} & = &-12 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 10x-3x& = &-12+30 \\\Leftrightarrow & 7x& = &18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)