Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{9})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -21x+\frac{35}{9}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-378}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -378x \color{red}{+70} & = & \color{red}{144x} +63 \\\Leftrightarrow & -378x \color{red}{+70} \color{blue}{-70} \color{blue}{-144x} & = & \color{red}{144x} +63 \color{blue}{-144x} \color{blue}{-70} \\\Leftrightarrow & -378x-144x& = & 63-70 \\\Leftrightarrow & \color{red}{-522} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-522} & & \\\Leftrightarrow & x = \frac{7}{522} & & \\ & V = \left\{ \frac{7}{522} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -3x+\frac{5}{6} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{+72} & = & \color{red}{-90x} +25 \\\Leftrightarrow & 600x \color{red}{+72} \color{blue}{-72} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{-72} \\\Leftrightarrow & 600x+90x& = & 25-72 \\\Leftrightarrow & \color{red}{690} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{690} & & \\ & V = \left\{ \frac{-47}{690} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{9})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -10x+\frac{10}{9}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-720}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{-504x} +63 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{+504x} & = & \color{red}{-504x} +63 \color{blue}{+504x} \color{blue}{-80} \\\Leftrightarrow & -720x+504x& = & 63-80 \\\Leftrightarrow & \color{red}{-216} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-216} & & \\\Leftrightarrow & x = \frac{17}{216} & & \\ & V = \left\{ \frac{17}{216} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{231x} +88 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & -990x-231x& = & 88+54 \\\Leftrightarrow & \color{red}{-1221} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-1221} & & \\\Leftrightarrow & x = \frac{-142}{1221} & & \\ & V = \left\{ \frac{-142}{1221} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -20x-\frac{10}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-70} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -1540x \color{red}{-70} \color{blue}{+70} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+70} \\\Leftrightarrow & -1540x+539x& = & 110+70 \\\Leftrightarrow & \color{red}{-1001} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-1001} & & \\\Leftrightarrow & x = \frac{-180}{1001} & & \\ & V = \left\{ \frac{-180}{1001} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & 9x+\frac{4}{11} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+44} & = & \color{red}{495x} +20 \\\Leftrightarrow & -440x \color{red}{+44} \color{blue}{-44} \color{blue}{-495x} & = & \color{red}{495x} +20 \color{blue}{-495x} \color{blue}{-44} \\\Leftrightarrow & -440x-495x& = & 20-44 \\\Leftrightarrow & \color{red}{-935} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-935} & & \\\Leftrightarrow & x = \frac{24}{935} & & \\ & V = \left\{ \frac{24}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{3})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 8x+\frac{16}{3}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x+ \frac{160}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{+160} & = & \color{red}{210x} +27 \\\Leftrightarrow & 240x \color{red}{+160} \color{blue}{-160} \color{blue}{-210x} & = & \color{red}{210x} +27 \color{blue}{-210x} \color{blue}{-160} \\\Leftrightarrow & 240x-210x& = & 27-160 \\\Leftrightarrow & \color{red}{30} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{30} & & \\ & V = \left\{ \frac{-133}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-30} & = & \color{red}{-385x} +77 \\\Leftrightarrow & -550x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +77 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & -550x+385x& = & 77+30 \\\Leftrightarrow & \color{red}{-165} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-165} & & \\\Leftrightarrow & x = \frac{-107}{165} & & \\ & V = \left\{ \frac{-107}{165} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{9})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{4}{9}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+4} & = & \color{red}{81x} +24 \\\Leftrightarrow & -72x \color{red}{+4} \color{blue}{-4} \color{blue}{-81x} & = & \color{red}{81x} +24 \color{blue}{-81x} \color{blue}{-4} \\\Leftrightarrow & -72x-81x& = & 24-4 \\\Leftrightarrow & \color{red}{-153} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-153} & & \\\Leftrightarrow & x = \frac{-20}{153} & & \\ & V = \left\{ \frac{-20}{153} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{11})& = & -3x+\frac{5}{4} \\\Leftrightarrow & -8x-\frac{10}{11}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{-40} & = & \color{red}{-132x} +55 \\\Leftrightarrow & -352x \color{red}{-40} \color{blue}{+40} \color{blue}{+132x} & = & \color{red}{-132x} +55 \color{blue}{+132x} \color{blue}{+40} \\\Leftrightarrow & -352x+132x& = & 55+40 \\\Leftrightarrow & \color{red}{-220} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-220} & & \\\Leftrightarrow & x = \frac{-19}{44} & & \\ & V = \left\{ \frac{-19}{44} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{8})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{15}{8}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{-165} & = & \color{red}{-440x} +48 \\\Leftrightarrow & -792x \color{red}{-165} \color{blue}{+165} \color{blue}{+440x} & = & \color{red}{-440x} +48 \color{blue}{+440x} \color{blue}{+165} \\\Leftrightarrow & -792x+440x& = & 48+165 \\\Leftrightarrow & \color{red}{-352} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-352} & & \\\Leftrightarrow & x = \frac{-213}{352} & & \\ & V = \left\{ \frac{-213}{352} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{-80x} +15 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{+80x} & = & \color{red}{-80x} +15 \color{blue}{+80x} \color{blue}{-24} \\\Leftrightarrow & -150x+80x& = & 15-24 \\\Leftrightarrow & \color{red}{-70} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-70} & & \\\Leftrightarrow & x = \frac{9}{70} & & \\ & V = \left\{ \frac{9}{70} \right\} & \\\end{align}\)