Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & 9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+2}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+4x } & = & -8 \color{red}{ -4x }\color{blue}{-2+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+9}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-13x } & = & 1 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-9}& = & 8 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+10x } & = & 8 \color{red}{ -10x }\color{blue}{+9+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &17x & = &17\\\Leftrightarrow & \color{red}{17}x & = &17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{17}{17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+11}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+15x } & = & 3 \color{red}{ -15x }\color{blue}{-11+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &19x & = &-8\\\Leftrightarrow & \color{red}{19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & 10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x } & = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+12}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-7x } & = & -13 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &-20x & = &-25\\\Leftrightarrow & \color{red}{-20}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-25}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-2}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-14x } & = & 3 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-7}& = & 1 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+15x } & = & 1 \color{red}{ -15x }\color{blue}{+7+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &16x & = &8\\\Leftrightarrow & \color{red}{16}x & = &8\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{8}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)