Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-5}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-13x } & = & 4 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & -2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+12}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+7x } & = & -3 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &12x & = &-15\\\Leftrightarrow & \color{red}{12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 15 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-5x & = &20\\\Leftrightarrow & \color{red}{-5}x & = &20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{20}{-5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-15}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-14x } & = & 4 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-27x & = &19\\\Leftrightarrow & \color{red}{-27}x & = &19\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{19}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{27} } & & \\ & V = \left\{ \frac{-19}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-7}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+8x } & = & 8 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &17x & = &15\\\Leftrightarrow & \color{red}{17}x & = &15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-4}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-10x } & = & 11 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-x } & = & -4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-8}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-4x } & = & -1 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-12}& = & 4 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+14x } & = & 4 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &29x & = &16\\\Leftrightarrow & \color{red}{29}x & = &16\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{16}{29} \\\Leftrightarrow & \color{green}{ x = \frac{16}{29} } & & \\ & V = \left\{ \frac{16}{29} \right\} & \\\end{align}\)