Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & -9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-8}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-11x } & = & 12 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-16x & = &20\\\Leftrightarrow & \color{red}{-16}x & = &20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & -2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+2}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-11x } & = & -3 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+15}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15-8x } & = & 11 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-2}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+9x } & = & -6 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &14x & = &-4\\\Leftrightarrow & \color{red}{14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+10}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-4x } & = & -11 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &5x & = &-21\\\Leftrightarrow & \color{red}{5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-21}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & -15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-16x & = &-19\\\Leftrightarrow & \color{red}{-16}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{19}{16} } & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+5}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5+11x } & = & -11 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &23x & = &-16\\\Leftrightarrow & \color{red}{23}x & = &-16\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-16}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{23} } & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)