Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+5)& = & -7 \color{red}{-} (12+x) \\\Leftrightarrow & -30x+30& = &-7-12-x \\\Leftrightarrow & -30x \color{red}{+30} & = &-19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &-19-30 \\\Leftrightarrow & -29x& = &-49 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-49}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{49}{29} & & \\ & V = \left\{ \frac{49}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x+4)& = & 2 \color{red}{-} (-11+x) \\\Leftrightarrow & -2x+8& = &2+11-x \\\Leftrightarrow & -2x \color{red}{+8} & = &13 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -2x+x& = &13-8 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x+2)& = & 6 \color{red}{+} (5-5x) \\\Leftrightarrow & 6x+6& = &6+5-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &11 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &11-6 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-7)& = & 11 \color{red}{-} (-5+x) \\\Leftrightarrow & -30x-42& = &11+5-x \\\Leftrightarrow & -30x \color{red}{-42} & = &16 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -30x+x& = &16+42 \\\Leftrightarrow & -29x& = &58 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{58}{ \color{red}{-29} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-1)& = & 10 \color{red}{+} (9+x) \\\Leftrightarrow & -18x-3& = &10+9+x \\\Leftrightarrow & -18x \color{red}{-3} & = &19 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -18x-x& = &19+3 \\\Leftrightarrow & -19x& = &22 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{22}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-22}{19} & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x+4)& = & -14 \color{red}{+} (-7-2x) \\\Leftrightarrow & 15x+12& = &-14-7-2x \\\Leftrightarrow & 15x \color{red}{+12} & = &-21 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &-21 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & 15x+2x& = &-21-12 \\\Leftrightarrow & 17x& = &-33 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-33}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-33}{17} & & \\ & V = \left\{ \frac{-33}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+3)& = & -2 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x+12& = &-2-4+x \\\Leftrightarrow & -20x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -20x-x& = &-6-12 \\\Leftrightarrow & -21x& = &-18 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-18}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-1)& = & 11 \color{red}{+} (5-5x) \\\Leftrightarrow & -6x-2& = &11+5-5x \\\Leftrightarrow & -6x \color{red}{-2} & = &16 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+2} \\\Leftrightarrow & -6x+5x& = &16+2 \\\Leftrightarrow & -x& = &18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{18}{ \color{red}{-1} } \\\Leftrightarrow & x = -18 & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x+1)& = & -4 \color{red}{-} (8-2x) \\\Leftrightarrow & -9x+3& = &-4-8+2x \\\Leftrightarrow & -9x \color{red}{+3} & = &-12 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -9x-2x& = &-12-3 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-6)& = & -12 \color{red}{-} (8+x) \\\Leftrightarrow & -16x-24& = &-12-8-x \\\Leftrightarrow & -16x \color{red}{-24} & = &-20 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -16x+x& = &-20+24 \\\Leftrightarrow & -15x& = &4 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{4}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-3)& = & -6 \color{red}{+} (10+x) \\\Leftrightarrow & -4x-6& = &-6+10+x \\\Leftrightarrow & -4x \color{red}{-6} & = &4 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -4x-x& = &4+6 \\\Leftrightarrow & -5x& = &10 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{10}{ \color{red}{-5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+1)& = & 14 \color{red}{-} (12+x) \\\Leftrightarrow & 12x+2& = &14-12-x \\\Leftrightarrow & 12x \color{red}{+2} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 12x+x& = &2-2 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)