Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x-7)& = & 9 \color{red}{-} (-6-5x) \\\Leftrightarrow & 18x-42& = &9+6+5x \\\Leftrightarrow & 18x \color{red}{-42} & = &15 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 18x-5x& = &15+42 \\\Leftrightarrow & 13x& = &57 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{57}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{57}{13} & & \\ & V = \left\{ \frac{57}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x-5)& = & 8 \color{red}{+} (12-5x) \\\Leftrightarrow & -6x-10& = &8+12-5x \\\Leftrightarrow & -6x \color{red}{-10} & = &20 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+10} \\\Leftrightarrow & -6x+5x& = &20+10 \\\Leftrightarrow & -x& = &30 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{30}{ \color{red}{-1} } \\\Leftrightarrow & x = -30 & & \\ & V = \left\{ -30 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+2)& = & 7 \color{red}{-} (-14-3x) \\\Leftrightarrow & -25x+10& = &7+14+3x \\\Leftrightarrow & -25x \color{red}{+10} & = &21 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -25x-3x& = &21-10 \\\Leftrightarrow & -28x& = &11 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{11}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{-11}{28} & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+1)& = & -3 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+3& = &-3-4+x \\\Leftrightarrow & -12x \color{red}{+3} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &-7-3 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+4)& = & -13 \color{red}{-} (-14+x) \\\Leftrightarrow & 15x+20& = &-13+14-x \\\Leftrightarrow & 15x \color{red}{+20} & = &1 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 15x+x& = &1-20 \\\Leftrightarrow & 16x& = &-19 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-19}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-19}{16} & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+6)& = & -10 \color{red}{-} (4+x) \\\Leftrightarrow & 4x+12& = &-10-4-x \\\Leftrightarrow & 4x \color{red}{+12} & = &-14 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 4x+x& = &-14-12 \\\Leftrightarrow & 5x& = &-26 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-26}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-26}{5} & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+4)& = & 12 \color{red}{-} (-10-5x) \\\Leftrightarrow & -6x+12& = &12+10+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &22 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &22-12 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x+2)& = & 13 \color{red}{+} (-11+x) \\\Leftrightarrow & 15x+6& = &13-11+x \\\Leftrightarrow & 15x \color{red}{+6} & = &2 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 15x-x& = &2-6 \\\Leftrightarrow & 14x& = &-4 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-4}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+6)& = & -1 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+36& = &-1+8+x \\\Leftrightarrow & -12x \color{red}{+36} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -12x-x& = &7-36 \\\Leftrightarrow & -13x& = &-29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+3)& = & -15 \color{red}{-} (12-3x) \\\Leftrightarrow & 4x+6& = &-15-12+3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-27 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-27 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 4x-3x& = &-27-6 \\\Leftrightarrow & x& = &-33 \\ & V = \left\{ -33 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+5)& = & -4 \color{red}{-} (5+x) \\\Leftrightarrow & 9x+15& = &-4-5-x \\\Leftrightarrow & 9x \color{red}{+15} & = &-9 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 9x+x& = &-9-15 \\\Leftrightarrow & 10x& = &-24 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-24}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x-6)& = & 7 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-36& = &7-14+x \\\Leftrightarrow & -24x \color{red}{-36} & = &-7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -24x-x& = &-7+36 \\\Leftrightarrow & -25x& = &29 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{29}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-29}{25} & & \\ & V = \left\{ \frac{-29}{25} \right\} & \\\end{align}\)