Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-16\\\Leftrightarrow & \color{red}{-6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-12}& = & -12 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+4x } & = & -12 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-12}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-4x } & = & 9 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &3x & = &21\\\Leftrightarrow & \color{red}{3}x & = &21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{21}{3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-x } & = & -4 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-4}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+11x } & = & 11 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &26x & = &15\\\Leftrightarrow & \color{red}{26}x & = &15\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{15}{26} \\\Leftrightarrow & \color{green}{ x = \frac{15}{26} } & & \\ & V = \left\{ \frac{15}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+10}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+4x } & = & -8 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-8}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+11x } & = & -9 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &12x & = &-1\\\Leftrightarrow & \color{red}{12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x } & = & 11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+2}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-4x } & = & -3 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-12}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-5x } & = & 5 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+7}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-13x } & = & -14 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-28x & = &-21\\\Leftrightarrow & \color{red}{-28}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-21}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)