Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+1}& = &-15 \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+8}& = &15 \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8} & = &15\color{blue}{-8} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-9}& = &8 \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9} & = &8\color{blue}{+9} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+9}& = &14 \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9} & = &14\color{blue}{-9} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-10}& = &7 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &7\color{blue}{+10} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+14}& = &-12 \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14} & = &-12\color{blue}{-14} \\\Leftrightarrow &4x & = &-26\\\Leftrightarrow & \color{red}{4}x & = &-26\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-26}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-6}& = &4 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6} & = &4\color{blue}{+6} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+10}& = &7 \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-4}& = &-11 \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4} & = &-11\color{blue}{+4} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-5}& = &11 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &11\color{blue}{+5} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-3}& = &14 \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &9x & = &17\\\Leftrightarrow & \color{red}{9}x & = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+2}& = &-12 \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2} & = &-12\color{blue}{-2} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)