Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+3)& = & -1 \color{red}{-} (14-2x) \\\Leftrightarrow & 15x+9& = &-1-14+2x \\\Leftrightarrow & 15x \color{red}{+9} & = &-15 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &-15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & 15x-2x& = &-15-9 \\\Leftrightarrow & 13x& = &-24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x+4)& = & 8 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+24& = &8+6+x \\\Leftrightarrow & 12x \color{red}{+24} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &14-24 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+7)& = & -12 \color{red}{-} (6-3x) \\\Leftrightarrow & -10x+35& = &-12-6+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &-18 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &-18-35 \\\Leftrightarrow & -13x& = &-53 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-53}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{53}{13} & & \\ & V = \left\{ \frac{53}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-1)& = & -12 \color{red}{+} (-13-3x) \\\Leftrightarrow & 10x-2& = &-12-13-3x \\\Leftrightarrow & 10x \color{red}{-2} & = &-25 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 10x+3x& = &-25+2 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x+7)& = & -7 \color{red}{+} (-13+x) \\\Leftrightarrow & 10x+14& = &-7-13+x \\\Leftrightarrow & 10x \color{red}{+14} & = &-20 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 10x-x& = &-20-14 \\\Leftrightarrow & 9x& = &-34 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-34}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-34}{9} & & \\ & V = \left\{ \frac{-34}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-1)& = & 7 \color{red}{+} (14+x) \\\Leftrightarrow & -24x-6& = &7+14+x \\\Leftrightarrow & -24x \color{red}{-6} & = &21 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -24x-x& = &21+6 \\\Leftrightarrow & -25x& = &27 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{27}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-27}{25} & & \\ & V = \left\{ \frac{-27}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x-5)& = & 4 \color{red}{+} (12+x) \\\Leftrightarrow & -6x-15& = &4+12+x \\\Leftrightarrow & -6x \color{red}{-15} & = &16 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &16+15 \\\Leftrightarrow & -7x& = &31 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{31}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x+1)& = & 4 \color{red}{-} (-8-5x) \\\Leftrightarrow & 8x+2& = &4+8+5x \\\Leftrightarrow & 8x \color{red}{+2} & = &12 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 8x-5x& = &12-2 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x+4)& = & 5 \color{red}{+} (-4-5x) \\\Leftrightarrow & 6x+24& = &5-4-5x \\\Leftrightarrow & 6x \color{red}{+24} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 6x+5x& = &1-24 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-5)& = & 2 \color{red}{+} (-3+3x) \\\Leftrightarrow & -4x-10& = &2-3+3x \\\Leftrightarrow & -4x \color{red}{-10} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -4x-3x& = &-1+10 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-2)& = & 6 \color{red}{-} (-13+x) \\\Leftrightarrow & 9x-6& = &6+13-x \\\Leftrightarrow & 9x \color{red}{-6} & = &19 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 9x+x& = &19+6 \\\Leftrightarrow & 10x& = &25 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{25}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+1)& = & -2 \color{red}{-} (5+x) \\\Leftrightarrow & 12x+6& = &-2-5-x \\\Leftrightarrow & 12x \color{red}{+6} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &-7-6 \\\Leftrightarrow & 13x& = &-13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-13}{ \color{red}{13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)