Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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