Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-x } & = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-11}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-3x } & = & -8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-30\\\Leftrightarrow & \color{red}{-15}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-30}{-15} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-9}& = & 6 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+2x } & = & 6 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &9x & = &15\\\Leftrightarrow & \color{red}{9}x & = &15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-11}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x } & = & -1 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-3}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3+13x } & = & 9 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &23x & = &12\\\Leftrightarrow & \color{red}{23}x & = &12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{12}{23} } & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+6}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-8x } & = & 8 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+8}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & 4 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & 6 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)