Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x+2)& = & 13 \color{red}{-} (13-2x) \\\Leftrightarrow & -15x+6& = &13-13+2x \\\Leftrightarrow & -15x \color{red}{+6} & = &0 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -15x-2x& = &0-6 \\\Leftrightarrow & -17x& = &-6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-4)& = & -13 \color{red}{-} (-4+x) \\\Leftrightarrow & -36x-24& = &-13+4-x \\\Leftrightarrow & -36x \color{red}{-24} & = &-9 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -36x+x& = &-9+24 \\\Leftrightarrow & -35x& = &15 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{15}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x-5)& = & -11 \color{red}{-} (7+3x) \\\Leftrightarrow & 2x-10& = &-11-7-3x \\\Leftrightarrow & 2x \color{red}{-10} & = &-18 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 2x+3x& = &-18+10 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-6)& = & -2 \color{red}{+} (15+x) \\\Leftrightarrow & -6x-12& = &-2+15+x \\\Leftrightarrow & -6x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &13+12 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+1)& = & 15 \color{red}{-} (10+4x) \\\Leftrightarrow & 3x+3& = &15-10-4x \\\Leftrightarrow & 3x \color{red}{+3} & = &5 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 3x+4x& = &5-3 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x+4)& = & 13 \color{red}{-} (-13-4x) \\\Leftrightarrow & -25x+20& = &13+13+4x \\\Leftrightarrow & -25x \color{red}{+20} & = &26 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &26 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -25x-4x& = &26-20 \\\Leftrightarrow & -29x& = &6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x+1)& = & -5 \color{red}{+} (2+x) \\\Leftrightarrow & 4x+4& = &-5+2+x \\\Leftrightarrow & 4x \color{red}{+4} & = &-3 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 4x-x& = &-3-4 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+4)& = & 2 \color{red}{+} (-15-4x) \\\Leftrightarrow & 5x+20& = &2-15-4x \\\Leftrightarrow & 5x \color{red}{+20} & = &-13 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &-13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & 5x+4x& = &-13-20 \\\Leftrightarrow & 9x& = &-33 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-33}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x+3)& = & 15 \color{red}{+} (-3+x) \\\Leftrightarrow & 6x+18& = &15-3+x \\\Leftrightarrow & 6x \color{red}{+18} & = &12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 6x-x& = &12-18 \\\Leftrightarrow & 5x& = &-6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x+4)& = & 15 \color{red}{-} (-7+x) \\\Leftrightarrow & 4x+16& = &15+7-x \\\Leftrightarrow & 4x \color{red}{+16} & = &22 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 4x+x& = &22-16 \\\Leftrightarrow & 5x& = &6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+7)& = & 13 \color{red}{+} (-13+x) \\\Leftrightarrow & -36x+42& = &13-13+x \\\Leftrightarrow & -36x \color{red}{+42} & = &0 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -36x-x& = &0-42 \\\Leftrightarrow & -37x& = &-42 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-42}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{42}{37} & & \\ & V = \left\{ \frac{42}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-4)& = & -3 \color{red}{+} (2+x) \\\Leftrightarrow & -30x-24& = &-3+2+x \\\Leftrightarrow & -30x \color{red}{-24} & = &-1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -30x-x& = &-1+24 \\\Leftrightarrow & -31x& = &23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-23}{31} & & \\ & V = \left\{ \frac{-23}{31} \right\} & \\\end{align}\)