Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x } & = & -6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-4}& = & 10 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+10x } & = & 10 \color{red}{ -10x }\color{blue}{+4+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & -8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+4}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+7x } & = & 5 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &22x & = &1\\\Leftrightarrow & \color{red}{22}x & = &1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{22} } & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-11}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-11x } & = & 12 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+5}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-11x } & = & 6 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-12}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+7x } & = & 2 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+8}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & -3 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-6}& = & 6 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-10x } & = & 6 \color{red}{ +10x }\color{blue}{+6-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & 3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-8x & = &-17\\\Leftrightarrow & \color{red}{-8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+15}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-8x } & = & -14 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-29\\\Leftrightarrow & \color{red}{-23}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-29}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{29}{23} } & & \\ & V = \left\{ \frac{29}{23} \right\} & \\\end{align}\)