Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+11}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11+13x } & = & -10 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &22x & = &-21\\\Leftrightarrow & \color{red}{22}x & = &-21\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-21}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{22} } & & \\ & V = \left\{ \frac{-21}{22} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-15}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-4x } & = & 11 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-1}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-13x } & = & -2 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-28x & = &-1\\\Leftrightarrow & \color{red}{-28}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{28} } & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+7}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-11x } & = & -6 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+13}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-3x } & = & 12 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+8}& = & 8 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x } & = & 8 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & -11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-15}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x } & = & 6 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-18x & = &21\\\Leftrightarrow & \color{red}{-18}x & = &21\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{21}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-2}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-13x } & = & -12 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & -9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)