Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & -5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-2}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2+7x } & = & 7 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-8}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-3x } & = & 2 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-1}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-3x } & = & 4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-2}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2+13x } & = & 7 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &27x & = &9\\\Leftrightarrow & \color{red}{27}x & = &9\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{9}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & 7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & -12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-12}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-13x } & = & 2 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-7x & = &14\\\Leftrightarrow & \color{red}{-7}x & = &14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{14}{-7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-10}& = & 5 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10+15x } & = & 5 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &23x & = &15\\\Leftrightarrow & \color{red}{23}x & = &15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-10\\\Leftrightarrow & \color{red}{-4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-4}& = & 5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+6x } & = & 5 \color{red}{ -6x }\color{blue}{+4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &19x & = &9\\\Leftrightarrow & \color{red}{19}x & = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)