Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & 9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-29\\\Leftrightarrow & \color{red}{-8}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-29}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{29}{8} } & & \\ & V = \left\{ \frac{29}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+13}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+13x } & = & -2 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &22x & = &-15\\\Leftrightarrow & \color{red}{22}x & = &-15\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-15}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{22} } & & \\ & V = \left\{ \frac{-15}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-3}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-3x } & = & 14 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &2x & = &17\\\Leftrightarrow & \color{red}{2}x & = &17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-1}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-9x } & = & 7 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-20x & = &8\\\Leftrightarrow & \color{red}{-20}x & = &8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+13}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-9x } & = & -5 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & 1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+2}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-8x } & = & 5 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & 6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+7}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7+7x } & = & 14 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)