Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+5}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-6x } & = & 11 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &2x & = &-5\\\Leftrightarrow & \color{red}{2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+12}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12-3x } & = & -11 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-2x & = &-23\\\Leftrightarrow & \color{red}{-2}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{23}{2} } & & \\ & V = \left\{ \frac{23}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+5}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+6x } & = & -12 \color{red}{ -6x }\color{blue}{-5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-8}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-3x } & = & -5 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+3}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+7x } & = & 13 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &15x & = &10\\\Leftrightarrow & \color{red}{15}x & = &10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-3}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x } & = & 11 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &23x & = &14\\\Leftrightarrow & \color{red}{23}x & = &14\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{14}{23} \\\Leftrightarrow & \color{green}{ x = \frac{14}{23} } & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+3}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+13x } & = & 5 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &24x & = &2\\\Leftrightarrow & \color{red}{24}x & = &2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-x } & = & 14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)