Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{4}{7})& = & -3x+\frac{7}{11} \\\Leftrightarrow & 14x+4& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{154}{ \color{blue}{11} }x+ \frac{44}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 154x \color{red}{+44} & = & \color{red}{-33x} +7 \\\Leftrightarrow & 154x \color{red}{+44} \color{blue}{-44} \color{blue}{+33x} & = & \color{red}{-33x} +7 \color{blue}{+33x} \color{blue}{-44} \\\Leftrightarrow & 154x+33x& = & 7-44 \\\Leftrightarrow & \color{red}{187} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{187} & & \\ & V = \left\{ \frac{-37}{187} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-30} \\\Leftrightarrow & 198x+165x& = & 44-30 \\\Leftrightarrow & \color{red}{363} x& = & 14 \\\Leftrightarrow & x = \frac{14}{363} & & \\ & V = \left\{ \frac{14}{363} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & 9x+\frac{5}{12} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{-32} & = & \color{red}{324x} +15 \\\Leftrightarrow & -288x \color{red}{-32} \color{blue}{+32} \color{blue}{-324x} & = & \color{red}{324x} +15 \color{blue}{-324x} \color{blue}{+32} \\\Leftrightarrow & -288x-324x& = & 15+32 \\\Leftrightarrow & \color{red}{-612} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-612} & & \\\Leftrightarrow & x = \frac{-47}{612} & & \\ & V = \left\{ \frac{-47}{612} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{4})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -14x+\frac{35}{4}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-56}{ \color{blue}{4} }x+ \frac{35}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -56x \color{red}{+35} & = & \color{red}{-12x} +6 \\\Leftrightarrow & -56x \color{red}{+35} \color{blue}{-35} \color{blue}{+12x} & = & \color{red}{-12x} +6 \color{blue}{+12x} \color{blue}{-35} \\\Leftrightarrow & -56x+12x& = & 6-35 \\\Leftrightarrow & \color{red}{-44} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-44} & & \\\Leftrightarrow & x = \frac{29}{44} & & \\ & V = \left\{ \frac{29}{44} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{135x} +40 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{-135x} & = & \color{red}{135x} +40 \color{blue}{-135x} \color{blue}{+36} \\\Leftrightarrow & 120x-135x& = & 40+36 \\\Leftrightarrow & \color{red}{-15} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-15} & & \\\Leftrightarrow & x = \frac{-76}{15} & & \\ & V = \left\{ \frac{-76}{15} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{11})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{-20} & = & \color{red}{66x} +55 \\\Leftrightarrow & 176x \color{red}{-20} \color{blue}{+20} \color{blue}{-66x} & = & \color{red}{66x} +55 \color{blue}{-66x} \color{blue}{+20} \\\Leftrightarrow & 176x-66x& = & 55+20 \\\Leftrightarrow & \color{red}{110} x& = & 75 \\\Leftrightarrow & x = \frac{75}{110} & & \\\Leftrightarrow & x = \frac{15}{22} & & \\ & V = \left\{ \frac{15}{22} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{7})& = & 8x+\frac{8}{11} \\\Leftrightarrow & -15x+\frac{9}{7}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+99} & = & \color{red}{616x} +56 \\\Leftrightarrow & -1155x \color{red}{+99} \color{blue}{-99} \color{blue}{-616x} & = & \color{red}{616x} +56 \color{blue}{-616x} \color{blue}{-99} \\\Leftrightarrow & -1155x-616x& = & 56-99 \\\Leftrightarrow & \color{red}{-1771} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-1771} & & \\\Leftrightarrow & x = \frac{43}{1771} & & \\ & V = \left\{ \frac{43}{1771} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+8} & = & \color{red}{21x} +8 \\\Leftrightarrow & 30x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & 30x-21x& = & 8-8 \\\Leftrightarrow & \color{red}{9} x& = & 0 \\\Leftrightarrow & x = \frac{0}{9} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{9})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{8}{9}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-16} & = & \color{red}{90x} +63 \\\Leftrightarrow & -216x \color{red}{-16} \color{blue}{+16} \color{blue}{-90x} & = & \color{red}{90x} +63 \color{blue}{-90x} \color{blue}{+16} \\\Leftrightarrow & -216x-90x& = & 63+16 \\\Leftrightarrow & \color{red}{-306} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-306} & & \\\Leftrightarrow & x = \frac{-79}{306} & & \\ & V = \left\{ \frac{-79}{306} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{11})& = & 6x+\frac{3}{10} \\\Leftrightarrow & 25x-\frac{25}{11}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2750}{ \color{blue}{110} }x- \frac{250}{ \color{blue}{110} })& = & (\frac{660}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2750x \color{red}{-250} & = & \color{red}{660x} +33 \\\Leftrightarrow & 2750x \color{red}{-250} \color{blue}{+250} \color{blue}{-660x} & = & \color{red}{660x} +33 \color{blue}{-660x} \color{blue}{+250} \\\Leftrightarrow & 2750x-660x& = & 33+250 \\\Leftrightarrow & \color{red}{2090} x& = & 283 \\\Leftrightarrow & x = \frac{283}{2090} & & \\ & V = \left\{ \frac{283}{2090} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{3})& = & 9x+\frac{6}{7} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+56} & = & \color{red}{189x} +18 \\\Leftrightarrow & 336x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +18 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & 336x-189x& = & 18-56 \\\Leftrightarrow & \color{red}{147} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{147} & & \\ & V = \left\{ \frac{-38}{147} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{28}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1575}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1575x \color{red}{-140} & = & \color{red}{135x} +54 \\\Leftrightarrow & -1575x \color{red}{-140} \color{blue}{+140} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{+140} \\\Leftrightarrow & -1575x-135x& = & 54+140 \\\Leftrightarrow & \color{red}{-1710} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-1710} & & \\\Leftrightarrow & x = \frac{-97}{855} & & \\ & V = \left\{ \frac{-97}{855} \right\} & \\\end{align}\)