Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-4}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-5x } & = & 4 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & -1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-11}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-7x } & = & 15 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-x & = &26\\\Leftrightarrow & \color{red}{-}x & = &26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{26}{-1} \\\Leftrightarrow & \color{green}{ x = -26 } & & \\ & V = \left\{ -26 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-12}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-5x } & = & -6 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-7}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+4x } & = & 1 \color{red}{ -4x }\color{blue}{+7+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+8}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-13x } & = & -2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-8}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-13x } & = & 9 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &-19x & = &17\\\Leftrightarrow & \color{red}{-19}x & = &17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &6x & = &-10\\\Leftrightarrow & \color{red}{6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x } & = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)