Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-10}& = & -5 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10+7x } & = & -5 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &15x & = &5\\\Leftrightarrow & \color{red}{15}x & = &5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-8}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-13x } & = & -15 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-15}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-8x } & = & 4 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-23x & = &19\\\Leftrightarrow & \color{red}{-23}x & = &19\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{19}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-13}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+13x } & = & -11 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+1}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+7x } & = & 10 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-10}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-13x } & = & 13 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-4x & = &23\\\Leftrightarrow & \color{red}{-4}x & = &23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-15}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+3x } & = & 14 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &10x & = &29\\\Leftrightarrow & \color{red}{10}x & = &29\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{29}{10} \\\Leftrightarrow & \color{green}{ x = \frac{29}{10} } & & \\ & V = \left\{ \frac{29}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-15}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-13x } & = & 2 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &-19x & = &17\\\Leftrightarrow & \color{red}{-19}x & = &17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+15}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-6x } & = & 2 \color{red}{ +6x }\color{blue}{-15-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-13\\\Leftrightarrow & \color{red}{-17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)