Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-132} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 990x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 990x+385x& = & 10+132 \\\Leftrightarrow & \color{red}{1375} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1375} & & \\ & V = \left\{ \frac{142}{1375} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{5}{12} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1800}{ \color{blue}{60} }x+ \frac{288}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1800x \color{red}{+288} & = & \color{red}{-420x} +25 \\\Leftrightarrow & 1800x \color{red}{+288} \color{blue}{-288} \color{blue}{+420x} & = & \color{red}{-420x} +25 \color{blue}{+420x} \color{blue}{-288} \\\Leftrightarrow & 1800x+420x& = & 25-288 \\\Leftrightarrow & \color{red}{2220} x& = & -263 \\\Leftrightarrow & x = \frac{-263}{2220} & & \\ & V = \left\{ \frac{-263}{2220} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{8})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{15}{8}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-144}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -144x \color{red}{-45} & = & \color{red}{-168x} +80 \\\Leftrightarrow & -144x \color{red}{-45} \color{blue}{+45} \color{blue}{+168x} & = & \color{red}{-168x} +80 \color{blue}{+168x} \color{blue}{+45} \\\Leftrightarrow & -144x+168x& = & 80+45 \\\Leftrightarrow & \color{red}{24} x& = & 125 \\\Leftrightarrow & x = \frac{125}{24} & & \\ & V = \left\{ \frac{125}{24} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{8}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-8} & = & \color{red}{77x} +5 \\\Leftrightarrow & -220x \color{red}{-8} \color{blue}{+8} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{+8} \\\Leftrightarrow & -220x-77x& = & 5+8 \\\Leftrightarrow & \color{red}{-297} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-297} & & \\\Leftrightarrow & x = \frac{-13}{297} & & \\ & V = \left\{ \frac{-13}{297} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & -9x+\frac{7}{12} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -9x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-80} & = & \color{red}{-108x} +7 \\\Leftrightarrow & -240x \color{red}{-80} \color{blue}{+80} \color{blue}{+108x} & = & \color{red}{-108x} +7 \color{blue}{+108x} \color{blue}{+80} \\\Leftrightarrow & -240x+108x& = & 7+80 \\\Leftrightarrow & \color{red}{-132} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-132} & & \\\Leftrightarrow & x = \frac{-29}{44} & & \\ & V = \left\{ \frac{-29}{44} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{15}{4}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+165} & = & \color{red}{-308x} +8 \\\Leftrightarrow & 528x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +8 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & 528x+308x& = & 8-165 \\\Leftrightarrow & \color{red}{836} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{836} & & \\ & V = \left\{ \frac{-157}{836} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 8x-\frac{16}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-16} & = & \color{red}{49x} +3 \\\Leftrightarrow & 56x \color{red}{-16} \color{blue}{+16} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{+16} \\\Leftrightarrow & 56x-49x& = & 3+16 \\\Leftrightarrow & \color{red}{7} x& = & 19 \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+14} & = & \color{red}{-24x} +2 \\\Leftrightarrow & 63x \color{red}{+14} \color{blue}{-14} \color{blue}{+24x} & = & \color{red}{-24x} +2 \color{blue}{+24x} \color{blue}{-14} \\\Leftrightarrow & 63x+24x& = & 2-14 \\\Leftrightarrow & \color{red}{87} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{87} & & \\\Leftrightarrow & x = \frac{-4}{29} & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 2x+\frac{4}{9} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 2x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{-108} & = & \color{red}{198x} +44 \\\Leftrightarrow & 1485x \color{red}{-108} \color{blue}{+108} \color{blue}{-198x} & = & \color{red}{198x} +44 \color{blue}{-198x} \color{blue}{+108} \\\Leftrightarrow & 1485x-198x& = & 44+108 \\\Leftrightarrow & \color{red}{1287} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1287} & & \\ & V = \left\{ \frac{152}{1287} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{900}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 900x \color{red}{-72} & = & \color{red}{210x} +25 \\\Leftrightarrow & 900x \color{red}{-72} \color{blue}{+72} \color{blue}{-210x} & = & \color{red}{210x} +25 \color{blue}{-210x} \color{blue}{+72} \\\Leftrightarrow & 900x-210x& = & 25+72 \\\Leftrightarrow & \color{red}{690} x& = & 97 \\\Leftrightarrow & x = \frac{97}{690} & & \\ & V = \left\{ \frac{97}{690} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{5})& = & 2x+\frac{10}{7} \\\Leftrightarrow & -28x+\frac{21}{5}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x+ \frac{147}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{+147} & = & \color{red}{70x} +50 \\\Leftrightarrow & -980x \color{red}{+147} \color{blue}{-147} \color{blue}{-70x} & = & \color{red}{70x} +50 \color{blue}{-70x} \color{blue}{-147} \\\Leftrightarrow & -980x-70x& = & 50-147 \\\Leftrightarrow & \color{red}{-1050} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-1050} & & \\\Leftrightarrow & x = \frac{97}{1050} & & \\ & V = \left\{ \frac{97}{1050} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{5})& = & 7x+\frac{7}{12} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1200}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1200x \color{red}{+144} & = & \color{red}{420x} +35 \\\Leftrightarrow & 1200x \color{red}{+144} \color{blue}{-144} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{-144} \\\Leftrightarrow & 1200x-420x& = & 35-144 \\\Leftrightarrow & \color{red}{780} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{780} & & \\ & V = \left\{ \frac{-109}{780} \right\} & \\\end{align}\)