Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-10}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-14x } & = & -1 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-6}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-7x } & = & -8 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-15}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-11x } & = & -11 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-10}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-14x } & = & -15 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-27x & = &-5\\\Leftrightarrow & \color{red}{-27}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-5}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{27} } & & \\ & V = \left\{ \frac{5}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+7}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7-10x } & = & -7 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-x & = &-14\\\Leftrightarrow & \color{red}{-}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-14}{-1} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+6}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+11x } & = & -6 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &26x & = &-12\\\Leftrightarrow & \color{red}{26}x & = &-12\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-12}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-10}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+5x } & = & 2 \color{red}{ -5x }\color{blue}{+10+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &16x & = &12\\\Leftrightarrow & \color{red}{16}x & = &12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-12}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-4x } & = & -4 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+6}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+2x } & = & 15 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & 11 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-12x } & = & 11 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)